If you doubt that God exists consider this:
His name is “I AM” (I exist).
When God called a reluctant Moses to lead his people out of slavery in Egypt, Moses asked God who should he say has sent him (Moses) — as in on whose authority because he didn’t think anyone would believe him otherwise. God replied:
“I AM who I AM. Say this to the people of Israel: I AM has sent me to you.” Exodus 3:14 NLT
"I AM" is a pretty cool name, and names have significant meaning in the Jewish tradition. So what do you say when God says to you "Why didn't you think I existed? My name is "I AM" -- I told you that." Hmmm... Awkward.