In a section on Biblical doctrine related to Jesus Christ's identity, The ESV Study Bible makes the following argument:
The ESV Study Bible - Biblical Doctrine: An Overview, The Person of Christ, The Humanity of Christ
Implications of the Two Natures of Christ
The belief that Jesus is one person with both divine and human natures has great significance for the possibility of fallen people entering into a relationship with God. Christ must be both God and man if he is to mediate between God and man, make atonement for sin, and be a sympathetic high priest (Col. 1:19-20: 1 Tim. 2:5, Heb. 2:17).
In his seminal work Why God Became Man, Anselm of Canterbury (c. A.D. 1033-1109) summarized the importance of the two natures of Christ for his atoning work by saying, "It is necessary that the self-same Person who is to make this satisfaction [for humanity's sins] be perfect God and perfect man, since He cannot make it unless He be really God, and He ought not to make it unless He be really man" (Book II, ch. 7).
The above states that Jesus "must be both God and man if he is to mediate between God and man". This is a common argument in Trinitarian apologetics, so it is worth taking the time to engage with.
Firstly, it is significant that no author of Scripture makes this argument. The verses cited by the ESV Study Bible do not make this claim:
Notice that each of the above passages explicitly distinguish Jesus from God. But, even if one were to grant that Jesus was God, it still would not follow that Jesus "must" have been God to reconcile mankind to God. That point is simply never made in Scripture.
And, there are other places in Scripture that describe God's plan to reconcile mankind to Himself, wherein Jesus is clearly distinguished from God in ways that would be very confusing if the authors intended their readers to believe that if Jesus were not God, the atonement would have been invalid:
John 3:16-17
16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
Romans 5:6-11
6 For when we were yet without strength, in due time Christ died for the ungodly.
7 For scarcely for a righteous man will one die: yet peradventure for a good man some would even dare to die.
8 But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.
9 Much more then, being now justified by his blood, we shall be saved from wrath through him.
10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.
11 And not only so, but we also joy in God through our Lord Jesus Christ, by whom we have now received the atonement.
Galatians 4:4-5
4 But when the fulness of the time was come, God sent forth his Son, made of a woman, made under the law,
5 To redeem them that were under the law, that we might receive the adoption of sons.
Notice how all three of the above passages speak of Jesus and God as separate subjects. The first century reader, unschooled in Trinitarian thought, would most naturally conclude that two different Beings are being spoken of in these places. And, if one of those Beings is God, and if there is "one God" (1 Timothy 2:5), then the other must not be God ("the man Christ Jesus").
This understanding also makes the most sense of Jesus being called a "mediator" between God and mankind. If Jesus is one Person, as the Bible everywhere portrays Him, then if He is Himself God, then sinful mankind would ultimately have no mediator with God. Instead, God would be mediating with His very same Being on behalf of mankind, in which case it is hard to see what meaning could be given to "mediation", given that only two parties are involved. Instead, 1 Timothy 2:5 presents Jesus as a third party between God and those in need of redemption.
The Bible never makes the argument that if Jesus were not God, the atonement would be invalid. This kind of argument is a later philosophical argument, and it stands upon a few layers of deduction and speculation.
Instead, the Bible, when speaking on the subject of the redemptive plan of God, clearly and without qualification distinguishes Jesus from God, and does so in ways that would naturally signal that they are distinct, and that Jesus is not God.