Does God's Existence Depend On What We Believe?

If I don't believe in God, does that mean He doesn't exist?
Does He need us to believe in him to exist, or his existence (or not) is independent from what we can believe?

My Reply:
If you don't believe in chocolate chip cookies, does that mean they don't exist?
If you're drowning, and I threw you a life-preserver, but yet you don't believe in life preservers, aren't you still drowning?

God exists, whether you believe in Him or not.

On that note though, won't you be saved from drowning if you grab onto the life preserver that you don't believe in, whether you believe it exists or not?  And if you're saved by it, then won't you in fact believe in them?  Just something to think about.