Something can't come from nothing.
Infinite regress is impossible.
A mind is needed to create a mind.
Hence, God exists.
Not proof. Faulty string of logic and assumptions that's been tried, repeatedly, and yet still fails. In particular, all assumptions are of questionable necessity to the argument, and the third just makes the conclusion circular and logically infeasible, for the version of God that you seek to support. Sadly, you don't just get to stop with "God" under those assumptions, regardless of how one tries to twist, if you assume that "God" has a mind.
And then comes another huge problem... saying that this "God" exists means absolutely nothing, unless you add on assumptions. Such as a mind of the type that would be required to do any of the things attributed to the Christian versions of God. Assumptions that have, it seems, been founded on nothing.
In short, the "God" that your argument suggests does not, in any way, coincide with the God that you seek to prove.
Edit: Also of enough relevance to repost:
You've been here one day and already I'm bored. Okay, I'll play two rounds and go to bed. I'll ask, why can't something come from nothing- didn't your God? You'll respond, He's existed forever. I'll ask, if so, why couldn't the Universe have existed forever? Etc.
Thank you for pointing out another of the contradictions inherent. In other words, then, the concept suggested as the answer to the logic completely violates two out of the three assumptions. That's far, far more than enough to say that that attempt fails. Utterly.