Short answer
No. Jesus said himself that he did not know when the Hour, the last day, would come. He said no one knows it, "neither the Son, but the Father". The Bible says God (﷾) "knoweth all things". Someone who does not know the Hour is not God. Christians reply that he did not know it only as a man. But they also say he is one person, God the Son. So the one they call God did not know. Even after what Christians call his resurrection, he said the times are in the Father's power. Islam gives the same answer. The Prophet Muhammad (ﷺ) said that the one asked about the Hour knows no more than the one asking. The Qur'an says its knowledge is with Allah (﷾) alone. Jesus and Muhammad (ﷺ) both said that only God (﷾) knows.
Full explanation
What Jesus said about the Hour
The Hour is the last day, when the world ends and the Day of Judgement begins. His disciples asked Jesus about the end. He said no one knows the day or the hour. The angels do not know it, and "neither the Son, but the Father". In Matthew he says the Father "only". The Bible says that God (﷾) "knoweth all things". One who does not know the day is not all-knowing. So on the Bible's own terms, he is not God.
“But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.”
“But of that day and hour knoweth no man, no, not the angels of heaven, but my Father only.”
“For if our heart condemn us, God is greater than our heart, and knoweth all things.”
The words that some copyists dropped
The oldest and best manuscripts of Matthew 24:36 also have "neither the Son". Manuscripts are the old hand-copied texts. Modern translations print these words. Most later manuscripts leave them out, and so does the King James Version shown here. Bruce Metzger, a leading scholar of New Testament manuscripts, wrote in his 1994 commentary that copyists more probably dropped the words than added them. He gave the reason: the words caused a difficulty for doctrine.
On Matthew 24:36, Metzger reports that the words "neither the Son" are found in the best early manuscripts of the Alexandrian and Western kinds but are missing from most later ones, and judges that copyists more probably dropped them because of the doctrinal difficulty than added them.
“But of that day and hour knoweth no man, no, not the angels of heaven, but my Father only.”
The two-natures reply
Christians answer that Christ has two natures, divine and human, in one person. As God (﷾) he knew all things. But in taking "the form of a servant" he accepted human limits. So he spoke of the day as a man. The Council of Chalcedon, a Church council in 451, made this the Church's official teaching.
“who, existing in the form of God, didn’t consider equality with God a thing to be grasped, but emptied himself, taking the form of a servant, being made in the likeness of men.”
The council confessed one and the same Christ in two natures, divine and human, and declared him "not parted or divided into two persons, but one and the same Son".
Who was the Son who did not know?
Christians say the one person, God the Son, knew the day in his divine mind but not in his human mind. But then one and the same person both knew and did not know the same thing. And Jesus did not say "my human mind does not know". He said "neither the Son". Suppose the reply is that someone else in Christ did not know. That makes two persons. The Church condemned that teaching under the name of Nestorius, bishop of Constantinople in the fifth century. The Council of Ephesus, in 431, removed him from office for dividing Christ in two. Chalcedon declared Christ "not parted or divided into two persons". Cyril of Alexandria, a fifth-century Church leader whose teaching won at Ephesus, said the Word of God, God the Son, suffered in the flesh. By the same rule, the Son who did not know the hour is the only Son there is.
The council confessed one and the same Christ in two natures, divine and human, and declared him "not parted or divided into two persons, but one and the same Son".
Cyril condemns anyone who does not confess that the Word of God suffered in the flesh, was crucified in the flesh and tasted death in the flesh. Cyril's teaching prevailed at the Council of Ephesus in 431, which deposed Nestorius, bishop of Constantinople, for dividing Christ into two.
“But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.”
Before he was taken up, he still points to the Father
There is a further problem for the two-natures reply. Acts tells of Jesus' last talk with his disciples, just before he was taken up. They asked whether he would now restore the kingdom to Israel. He answered that the times and seasons are in the Father's power. He did not say they were in his. The last book of the Bible opens by calling itself the revelation "which God gave unto him". Christians believe that book came from Jesus in heaven. Even there, what he knows of the future is given to him.
“When they therefore were come together, they asked of him, saying, Lord, wilt thou at this time restore again the kingdom to Israel? And he said unto them, It is not for you to know the times or the seasons, which the Father hath put in his own power.”
“And when he had spoken these things, while they beheld, he was taken up; and a cloud received him out of their sight.”
“The Revelation of Jesus Christ, which God gave unto him, to shew unto his servants things which must shortly come to pass; and he sent and signified it by his angel unto his servant John:”
The Prophet (ﷺ) answers Gabriel
Islam gives the same answer. The angel Gabriel asked the Prophet Muhammad (ﷺ) when the Hour would come. He answered that the one asked knew no more than the one asking. He then recited the verse that the knowledge of the Hour is with Allah (﷾) alone. The Qur'an commands him to give exactly that answer whenever people ask. Jesus and Muhammad (ﷺ) were each asked about the Hour. Both said that only God (﷾) knows it.
Abu Hurayra reports that the angel Gabriel came to the Prophet (ﷺ) in the form of a man and asked him about faith, Islam and excellence in worship, and then when the Hour would come. The Prophet answered that the one being asked knew no more about it than the one asking. He described some of its signs, said the Hour is one of five things that no one knows except Allah, and recited Qur'an 31:34.
“Verily the knowledge of the Hour is with Allah (alone). It is He Who sends down rain, and He Who knows what is in the wombs. Nor does any one know what it is that he will earn on the morrow: Nor does any one know in what land he is to die. Verily with Allah is full knowledge and He is acquainted (with all things).”
“They ask thee about the (final) Hour - when will be its appointed time? Say: "The knowledge thereof is with my Lord (alone): None but He can reveal as to when it will occur. Heavy were its burden through the heavens and the earth. Only, all of a sudden will it come to you." They ask thee as if thou Wert eager in search thereof: Say: "The knowledge thereof is with Allah (alone), but most men know not."”
Verse by verse
Mark 13:32 — Gospel of Mark, chapter 13, verse 32
“But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.”
Cited for
Jesus spoke here only in his human nature, during his earthly life. As God the Son he knew the day.
The response
The creeds allow only one "he" in Christ, God the Son. So it was God the Son who did not know. Even just before he is taken up, he does not claim the knowledge. He places the times in the Father's power. Revelation calls what he knows of the future something "God gave unto him".
Where it lands — The verse shows that Jesus did not know the Hour. The two-natures reply cannot remove that from the one person Christians call God.
Mark 13:32 — Gospel of Mark, chapter 13, verse 32
“But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.”
Cited for
Jesus did not lack the knowledge. He meant the day was not his to announce, as at a Jewish wedding, where the father set the day.
The response
The verse is about knowing, not announcing. No man knows the day, not the angels, neither the Son, but the Father. The same word, knoweth, covers all of them, and no one says the angels knew the day but were not allowed to tell it. In Matthew the Father "only" knows, so the Holy Spirit is left out too. And Jesus says nothing here about a wedding.
Where it lands — The verse names who knows the day, and it names the Father alone.
Perspectives
Mainstream Christian
Jesus is fully God and fully man, one person in two natures. As God he knew all things. In his human nature, during his earthly life, he did not know the day.
Paul says Christ took "the form of a servant" and was made in the likeness of men.
Rebuttal
Islam agrees that Jesus was a servant of God (﷾). But if God the Son took on limits and did not know the Hour, the one called God was not all-knowing. The Bible says God (﷾) "knoweth all things".
Christians hold that Jesus' ignorance of the day belonged to his human nature, not his divine nature.
Rebuttal
Jesus did not say "my human mind does not know"; he said "neither the Son". The creeds allow only one person in Christ, so the one they call God did not know. Even just before he was taken up, he still placed the times in the Father's power.
The Islamic perspective
Jesus was a prophet who knew what God (﷾) taught him. Only God (﷾) knows the Hour, as Jesus said, and as the Prophet Muhammad (ﷺ) said after him.
Jesus said that no one knows the day or the hour, "neither the Son, but the Father".
1 John 3:20 says God (﷾) "knoweth all things", and Mark 13:32 says the Son does not know the day.
One who does not know the Hour is not all-knowing, so he is not God.
Most later manuscripts of Matthew 24:36 drop "neither the Son". Metzger judges this was probably done for doctrinal reasons.
Just before he was taken up, Jesus still said the times are in the Father's power.
Revelation calls itself the revelation "which God gave unto him".
The Church condemned dividing Christ into two persons (Ephesus, 431) and defined him as one Son (Chalcedon, 451).
The creeds allow only one person in Christ, God the Son. So the two-natures reply leaves that one person both knowing and not knowing the Hour.
Gabriel asked the Prophet (ﷺ) when the Hour would come. He said the one asked knew no more than the one asking.
The Qur'an teaches that the knowledge of the Hour is with Allah (﷾) alone.