Short answer
Not as a scientific theory. But the Qur'an makes three statements that fit what astronomers now know. It says the heavens and the earth were once joined, and then God (﷾) parted them. It says the sky was once smoke. And it says God (﷾) makes the heaven vast. In 1929 the astronomer Edwin Hubble found that distant galaxies are moving away from us, the faster the farther they are. In 1964 two radio astronomers picked up the faint afterglow of the universe's hot beginning. The Qur'an is not a physics book. But these verses were revealed to the Prophet (ﷺ) thirteen centuries earlier. The creation account known around him had day and night, and even plants, before there was a sun. The Qur'an repeats neither mistake. Islam calls this a sign.
Full explanation
What the Qur'an says about the heavens
Three verses speak of the start and growth of the heavens. In 21:30 the heavens and the earth were ratq, sewn together as one, and God (﷾) split them apart (fatq). In 41:11 the sky "had been (as) smoke", the Arabic dukhan. In 51:47 God (﷾) built the heaven. The verse ends wa inna la-musi'un, from the root for wideness: "We are the ones who make it vast". Many modern translators render it "We are expanding it".
“Do not the Unbelievers see that the heavens and the earth were joined together (as one unit of creation), before we clove them asunder? We made from water every living thing. Will they not then believe?”
“Moreover He comprehended in His design the sky, and it had been (as) smoke: He said to it and to the earth: "Come ye together, willingly or unwillingly." They said: "We do come (together), in willing obedience."”
“With power and skill did We construct the Firmament: for it is We Who create the vastness of pace.”
What astronomy found
In 1929 the astronomer Edwin Hubble showed that the farther away a galaxy is, the faster it is moving away from us. Astronomers came to read this as the universe expanding. In 1964 two radio astronomers, Arno Penzias and Robert Wilson, found a faint radio glow coming from every direction in the sky. They published it in 1965. It is the leftover heat of the universe's hot, dense beginning, and it won them the Nobel Prize in 1978. Astronomers also know that the early universe was filled with hot gas. Stars still form from clouds of gas and dust.
Reports that the farther away a galaxy is, the faster it is moving away from us: the observation that became the evidence for an expanding universe.
Reports a faint, steady radio signal at 4080 megacycles coming equally from every direction in the sky, which they could not trace to their equipment. It was recognised as the cosmic microwave background, the afterglow of the hot early universe, and earned them the Nobel Prize in Physics in 1978.
The creation account known in Arabia
The Jews and Christians of the seventh century held Genesis, the first book of the Bible, to be the account of creation. Genesis has light, with day and night, on the first day. It has plants growing on the third day, and the sun made only on the fourth. The Bible also speaks of the pillars of the earth, which God (﷾) set the world upon and which tremble when He shakes it.
“And God said, Let there be light: and there was light. And God saw the light, that it was good: and God divided the light from the darkness. And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.”
“And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good. And the evening and the morning were the third day.”
“And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so. And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also. And God set them in the firmament of the heaven to give light upon the earth, And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good. And the evening and the morning were the fourth day.”
A French surgeon compares what the Bible and the Qur'an say about the natural world. On Genesis 1 he argues that a plant kingdom reproducing by seed could not have appeared before the sun existed, and that the Genesis order cannot be reconciled with established knowledge. He argues that the Qur'an's statements on the same subjects contain no such errors.
“for the pillars of the earth are the Lord’s, and he hath set the world upon them.”
“Which shaketh the earth out of her place, and the pillars thereof tremble.”
What the Qur'an does not say
The Qur'an never has day and night before the sun, and never puts plants before the sun. It says the sun and the moon each swim along in a rounded course. It never sets the earth on pillars. In 79:27-31 the earth's water and pasture are brought out after the heaven was built and its night and day were made. But 41:9-12 mentions the earth and its provision before God (﷾) turned to the heaven. The commentators, the scholars who explain the Qur'an, have discussed that order for centuries. Ibn Abbas, a Companion of the Prophet (ﷺ), read the two passages together. He said God (﷾) created the earth, then created and completed the heavens, and after that spread out the earth. What the Qur'an never says is that plants, or day and night, came before the sun.
“It is He Who created the Night and the Day, and the sun and the moon: all (the celestial bodies) swim along, each in its rounded course.”
“What! Are ye the more difficult to create or the heaven (above)? (Allah) hath constructed it: On high hath He raised its canopy, and He hath given it order and perfection. Its night doth He endow with darkness, and its splendour doth He bring out (with light). And the earth, moreover, hath He extended (to a wide expanse); He draweth out therefrom its moisture and its pasture;”
“Say: Is it that ye deny Him Who created the earth in two Days? And do ye join equals with Him? He is the Lord of (all) the Worlds. He set on the (earth), mountains standing firm, high above it, and bestowed blessings on the earth, and measure therein all things to give them nourishment in due proportion, in four Days, in accordance with (the needs of) those who seek (Sustenance). Moreover He comprehended in His design the sky, and it had been (as) smoke: He said to it and to the earth: "Come ye together, willingly or unwillingly." They said: "We do come (together), in willing obedience." So He completed them as seven firmaments in two Days, and He assigned to each heaven its duty and command. And We adorned the lower heaven with lights, and (provided it) with guard. Such is the Decree of (Him) the Exalted in Might, Full of Knowledge.”
A man brought the Companion Ibn Abbas verses that seemed to him to give different orders of creation, 41:9-12 and 79:27-30. Ibn Abbas answered that God created the earth in two days, then created the heaven and completed the heavens in two more days, and after that spread out the earth. Its spreading, he said, was that God brought out of it its water and its pasture. Al-Bukhari gives the report, with his own chain for it, at the head of the chapter on Surat Fussilat, just before hadith 4816.
A sign, not a proof-text
No one should claim that these verses teach the Big Bang theory. The claim is narrower than that. The Qur'an was revealed to the Prophet (ﷺ), a man who could not read, in Mecca in the early seventh century. It made plain statements about the heavens that sit well with what was found thirteen centuries later. The creation account known around him put day and night, and plants, before the sun, and the Bible set the earth on pillars. The Qur'an took on none of these. The Qur'an itself says God (﷾) will show His signs in the far horizons until it is clear that it is the truth.
“Do not the Unbelievers see that the heavens and the earth were joined together (as one unit of creation), before we clove them asunder? We made from water every living thing. Will they not then believe?”
“With power and skill did We construct the Firmament: for it is We Who create the vastness of pace.”
“And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so. And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also. And God set them in the firmament of the heaven to give light upon the earth, And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good. And the evening and the morning were the fourth day.”
“for the pillars of the earth are the Lord’s, and he hath set the world upon them.”
“Soon will We show them our Signs in the (furthest) regions (of the earth), and in their own souls, until it becomes manifest to them that this is the Truth. Is it not enough that thy Lord doth witness all things?”
The objection answered
Qur'an 41:9-12 — Surat Fussilat (Explained in detail), verses 9-12
“Say: Is it that ye deny Him Who created the earth in two Days? And do ye join equals with Him? He is the Lord of (all) the Worlds. He set on the (earth), mountains standing firm, high above it, and bestowed blessings on the earth, and measure therein all things to give them nourishment in due proportion, in four Days, in accordance with (the needs of) those who seek (Sustenance). Moreover He comprehended in His design the sky, and it had been (as) smoke: He said to it and to the earth: "Come ye together, willingly or unwillingly." They said: "We do come (together), in willing obedience." So He completed them as seven firmaments in two Days, and He assigned to each heaven its duty and command. And We adorned the lower heaven with lights, and (provided it) with guard. Such is the Decree of (Him) the Exalted in Might, Full of Knowledge.”
Cited for
Critics say 41:9-12 has the earth and its provision made before God turned to the sky, so the Qur'an has the same problem as Genesis.
The response
Ibn Abbas, the Companion of the Prophet (ﷺ), was asked about these verses. He said God (﷾) created the earth, then created and completed the heavens, and after that spread out the earth. That spreading was the bringing out of its water and pasture (79:30-31). The Qur'an also begins the heavens and the earth together, as one joined mass that God (﷾) parted (21:30). In 41:11 the sky is still smoke when God (﷾) turns to it. There God (﷾) speaks to the sky and the earth together. Then 41:12 speaks of completing it as seven heavens, which is a shaping and not a making from nothing.
Where it lands — The Qur'an never has plants, or day and night, before the sun, and it begins the heavens and the earth together.
Perspectives
The Islamic perspective
The Qur'an, revealed to the Prophet (ﷺ), speaks of the heavens in words that fit modern cosmology. It repeats neither the Genesis order of creation nor the pillars of the earth. That is a sign of where it came from.
The Qur'an says the heavens and the earth were joined together and then split apart.
The Qur'an says the sky was smoke (dukhan) when God (﷾) turned to it.
Qur'an 51:47 says God (﷾) built the heaven and makes it vast. The Arabic musi'un comes from the root for wideness and is widely translated "We are expanding it".
Astronomers established in the twentieth century that the universe is expanding and began hot and dense.
Genesis has plants on the third day and the sun on the fourth. The Qur'an puts the earth's water and pasture after the heaven's night and day.
The Bible speaks of the earth set on pillars; the Qur'an never sets the earth on pillars.
The Qur'an's statements about the heavens fit modern knowledge. They lack the mistakes of the creation account known around Arabia. This is a sign that the Qur'an is from God (﷾).