Short answer
No. The Bible never calls Jesus "the Creator". Most of the verses Christians cite say that all things were made "through" him. Paul, a Christian missionary of the first century, keeps the two apart. He writes of one God (﷾), the Father, "of whom are all things", and one Lord, Jesus, "through whom are all things". Jesus himself spoke of the Creator as someone else: "he which made them at the beginning". In the book of Isaiah, God (﷾) says He made all things "alone" and "by myself". That leaves no room for a partner in creation. The Qur'an gives the same answer: Allah (﷾) is the Creator of all things. Even the bird Jesus shaped from clay came to life only "by Allah's leave".
Full explanation
The verses Christians rely on
Christians read the opening of John's Gospel as saying that the Word, who is God, made everything. They take the Word to mean Jesus. Colossians, a New Testament letter, says all things were created by him and through him. Hebrews, another New Testament letter, says God (﷾) made the worlds through His Son. From these verses Christians conclude that the Son is the Creator together with the Father.
“In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made through him. Without him, nothing was made that has been made.”
“He is the image of the invisible God, the firstborn of all creation. For by him all things were created in the heavens and on the earth, visible things and invisible things, whether thrones or dominions or principalities or powers. All things have been created through him and for him.”
“has at the end of these days spoken to us by his Son, whom he appointed heir of all things, through whom also he made the worlds.”
"Of" the Father, "through" the Son
Paul, a Christian missionary of the first century, uses two different words in 1 Corinthians 8:6. All things are "of" the one God (﷾), the Father (Greek ex). They are "through" the one Lord, Jesus (Greek dia). The first word names the source. The second names the one through whom the work passes. The point is not the word "through" alone. Paul gives the name "one God", and "of whom", to the Father only. Hebrews says the same thing plainly: God (﷾) made the worlds through His Son. The one who makes is God.
“yet to us there is one God, the Father, of whom are all things, and we for him; and one Lord, Jesus Christ, through whom are all things, and we live through him.”
“has at the end of these days spoken to us by his Son, whom he appointed heir of all things, through whom also he made the worlds.”
Jesus named the Creator as someone else
Asked about marriage, Jesus pointed to "he which made them at the beginning". He spoke of the Creator as another, not as himself. Mark's account of the same words quotes Genesis. In Genesis, the one who made them male and female is God.
“And he answered and said unto them, Have ye not read, that he which made them at the beginning made them male and female,”
“But from the beginning of the creation God made them male and female.”
“So God created man in his own image, in the image of God created he him; male and female created he them.”
God (﷾) made all things alone
In the book of Isaiah, God (﷾) says He makes all things. He stretches out the heavens alone, and He spreads out the earth by Himself. Alone and by Himself leave no partner, and no one "through" whom. The Bible gives the title "the Creator" to God (﷾), who does not grow faint or weary.
“Thus saith the Lord, thy redeemer, and he that formed thee from the womb, I am the Lord that maketh all things; that stretcheth forth the heavens alone; that spreadeth abroad the earth by myself;”
“Hast thou not known? hast thou not heard, that the everlasting God, the Lord, the Creator of the ends of the earth, fainteth not, neither is weary? there is no searching of his understanding.”
Reading John as a partner would contradict Isaiah
Suppose John 1:3 is read as making the Word a partner in creation. Then it cannot stand beside Isaiah 44:24. Either God (﷾) made all things alone and by Himself, or He had a partner. The two readings cannot both be right. The God (﷾) of Isaiah, who creates alone, is the God (﷾) of the Qur'an.
“Thus saith the Lord, thy redeemer, and he that formed thee from the womb, I am the Lord that maketh all things; that stretcheth forth the heavens alone; that spreadeth abroad the earth by myself;”
“In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made through him. Without him, nothing was made that has been made.”
The Qur'an: one Creator
The Qur'an states that Allah (﷾) is the Creator of all things. It asks whether anyone has partners who created as He creates. It records Jesus' own words about his miracles. He shaped a bird from clay, and it became a bird by Allah's (﷾) leave.
“Allah is the Creator of all things, and He is the Guardian and Disposer of all affairs.”
“Or do they assign to Allah partners who have created (anything) as He has created, so that the creation seemed to them similar? Say: "Allah is the Creator of all things: He is the One, the Supreme and Irresistible."”
“I make for you out of clay, as it were, the figure of a bird, and breathe into it, and it becomes a bird by Allah's leave: And I heal those born blind, and the lepers, and I quicken the dead, by Allah's leave;”
Verse by verse
John 1:1-3 — Gospel of John, chapter 1, verses 1-3
“In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made through him. Without him, nothing was made that has been made.”
Cited for
The Word was God, and all things were made by him. So Jesus, the Word, is the Creator.
The response
The verse says all things were made "through" him. Paul uses the same word for Christ, and keeps "one God" and "of whom are all things" for the Father. Hebrews puts it plainly: God (﷾) made the worlds through His Son. The word "god" does not settle it either. God (﷾) told Moses, "I have made thee a god to Pharaoh."
Where it lands — John names the Word as the one through whom things were made. It does not call him the Creator, and Isaiah says the Creator worked alone.
Colossians 1:15-16 — Epistle to the Colossians, chapter 1, verses 15-16
“He is the image of the invisible God, the firstborn of all creation. For by him all things were created in the heavens and on the earth, visible things and invisible things, whether thrones or dominions or principalities or powers. All things have been created through him and for him.”
Cited for
All things were created by him, in heaven and on earth. Only the Creator could be described this way.
The response
The same verse ends: all things have been created "through him and for him". The verse before calls him "the image of the invisible God" and "the firstborn of all creation". It speaks of God (﷾) creating through him, as 1 Corinthians 8:6 does.
Where it lands — Colossians places creation through him. It does not make him the one God who, in Isaiah, made all things by Himself.
Hebrews 1:10 — Epistle to the Hebrews, chapter 1, verse 10
“And, Thou, Lord, in the beginning hast laid the foundation of the earth; and the heavens are the works of thine hands:”
Cited for
Hebrews applies to the Son a psalm about the Lord laying the foundation of the earth, so the Son is the Creator.
The response
The same chapter says God (﷾) made the worlds through the Son and appointed him heir. The verse just before says "God, even thy God, hath anointed thee". The one addressed has a God above him.
Where it lands — The chapter that quotes the psalm puts God (﷾) above the Son, so it cannot make him the God of Isaiah 44:24 who creates alone.
Perspectives
Mainstream Christian
Christians believe Jesus is the eternal Word, God the Son, through whom and by whom all things were made. They hold that he is Creator together with the Father.
John 1:3 and Colossians 1:16 say that all things were made through him. Christians read this as making him the Creator.
Rebuttal
Both verses do say all things were made through him. But 1 Corinthians 8:6 gives "one God" and "of whom are all things" to the Father alone, and only "through" to Jesus. Hebrews says God (﷾) made the worlds through His Son, and Isaiah 44:24 has God (﷾) making all things alone.
Christians read Hebrews 1:10, addressed to the Son, as making him the one who laid the foundation of the earth.
Rebuttal
The verse is addressed to the Son, but the same chapter says God (﷾) made the worlds through him. The verse just before says "God, even thy God, hath anointed thee": the one addressed has a God above him. So the chapter cannot make him the God of Isaiah 44:24, who creates alone.
The Islamic perspective
Allah (﷾) alone is the Creator. Jesus was His servant and messenger, and every miracle at his hands came by Allah's (﷾) leave.
God (﷾) says He made all things, stretching out the heavens alone and spreading out the earth by Himself.
Paul sets apart one God (﷾), the Father, of whom are all things. And he sets apart one Lord, Jesus, through whom are all things.
Hebrews says God (﷾) made the worlds through His Son, and that the Son has a God who anointed him.
Jesus spoke of the one who made mankind in the third person. The Genesis verse he quotes names Him as God.
The Bible gives the title "the Creator" to God (﷾) and never to Jesus by name.
The Qur'an teaches that Allah (﷾) is the Creator of all things. He has no partner who creates as He creates.
In the Qur'an Jesus says his miracles, even the bird of clay, happened only by Allah's (﷾) leave.