This is a question many folks ask. And the main pushback comes from the fact that, at first glance, nowhere in the Gospel accounts (Matthew, Mark, Luke, and John) does Jesus make the exact statement “I am God.”
But there is more than one way to claim divinity, and Jesus makes many direct and indirect claims about being divine.
One of the best summaries of these claims I have seen comes from Tim Keller (2016):1
There were all his indirect but deliberate claims. Jesus assumed authority to forgive all sins (Mark 2:7-10). Since we can forgive only sins that are against us, Jesus’s premise is that all sins are against him, and therefore that he is God, whose laws are broken and whose love is offended in every violation. Jesus also claimed that he alone could give eternal life (John 6:39-40), though God alone has the right to give or take life. More than that, Jesus claimed to have a power that could actually eliminate death, and he claimed not just to have or bring a power to raise the dead but to be the Power that can destroy death (John 11:25-26). Jesus claimed to have the truth as no one else ever has. All prophets said, “Thus saith the Lord,” but Jesus taught with “But I say unto you” out of his own authority (Mark 1:22; Luke 4:32). And more than that, he claimed not just to have or bring truth but to be the Truth itself, the source and locus of all truth (John 14:6).
Jesus assumed the authority to judge the world (Mark 14:62). Since God alone has both the infinite knowledge and the right (as creator and owner) to evaluate every person, Jesus’s premise is that he has both divine attributes. More than that, Jesus claimed that we will be judge in the end primarily on our attitude toward him (Matthew 10:32-33; John 3:18). Jesus assumed the right to receive worship (John 5:23, 9:38, 20:28-29; Luke 5:8), which neither great persons nor even angels would accept (Revelation 22:8-9; Acts 14:11-15). Even his offhand statements and actions continually assume that he has divine status. He comes to the temple and says all the rules about observing the Sabbath are off now because the inventor of the Sabbath is now here (mark 2:23-28). He puts his own knowledge on a par with God the Father’s (Matthew 11:27). He claimed to be perfectly sinless (John 8:46). He says that the greatest person in the history of the world was John the Baptist but that the weakest follower of Christ is greater than he (Matthew 11:11). This list could be stretched out indefinitely.
But then there are his direct claims, which are just as staggering. To know him is to know God (John 8:19), to see him was to see God (John 12:45), to receive him is to receive God (Mark 9:37). Only through him can anyone know or come to God (Matthew 11:27; John 14:6). Even when Jesus called himself “the Son of God” he was claiming equality with the Father, because in ancient times an only son inherited all the father’s wealth and position and was thus equal with him. the listeners knew that every time Jesus called him self “the Son,” he was naming himself as fully God (John 5:18). Finally, Jesus actually takes upon himself the divine name “I am” (John 8:58, Exodus 3:14, 6:3), claiming to be “Yahweh,” who appeared to Moses in the burning bush.” (pp. 238-239).
I hope this catalog is helpful.
Keller, T. (2016). Making Sense of God: An Invitation to the Skeptical.