No, God can't "mess things up" or commit sin of any kind. He is absolutely pure and holy, and there isn't even a hint of sin within Him. The Bible says, "Your eyes are too pure to look on evil; you cannot tolerate wrong" (Habakkuk 1:13).
Nor, the Bible says, did Jesus commit any sin. I know that's hard for us to understand; if we're honest, we know we sin every day. But Jesus was both fully human and fully divine - He was God in human flesh. Centuries before His birth, the prophet Isaiah foretold that "'The virgin will be with child and will give birth to a son, and they will call him Immanuel' - which means, 'God with us'" (Matthew 1:23).
And because Jesus was divine (as well as human), He never sinned. That doesn't mean He wasn't tempted - because He was (see Matthew 4:1-11). But He resisted the most intense temptations Satan could devise - and because He did, Jesus remained sinless to the end. The Bible says that He was "tempted in every way, just as we are - yet was without sin" (Hebrews 4:15). This is a profound mystery - but it's true.
Why is this important? The reason is because only a sinless, divine Savior could save us. He was without sin, but on the cross all our sins were placed on Him, and He took the judgment we deserve. He did this because God loves us. Are you trusting Christ alone for your salvation?