You're right when you say that God can do anything He wants to do -- and that means God could even stoop down and become a man. That's exactly what He did when Jesus Christ came into the world.
The Bible is clear: From all eternity, Jesus Christ was fully God -- all-powerful, all-knowing, all-loving, all-righteous. The Bible even tells us that the universe came into existence at Christ's command, and even now He sustains it. We can barely imagine this, but even the next breath you take is possible because of God's grace and power through Jesus Christ. The Bible says, "All things were created by him and for him. He is before all things, and in him all things hold together" (Colossians 1:16-17).
And yet Jesus Christ willingly gave up heaven's power and glory to come down to earth and become a man. As such, He was without sin, but He still got tired and hungry, and eventually He would die. The Bible says that Jesus, "Being in very nature God... made himself nothing, taking the very nature of a servant, being made in human likeness" (Philippians 2:6-7).
The real question, however, is this: Why did Jesus Christ come into the world? He came for one reason -- so you and I could have our sins forgiven, and go to be with Him in heaven forever. He did this by dying on the cross as the final sacrifice for our sins, and then conquering death by His resurrection. By faith commit your life to Him today.