An axiom: God is infinite. (True)

So let's study the action of creating that stone which God cannot lift up.
The stone would have to be of an infinite mass.
Therefore when God creates that stone, He would no longer exist.
Why? If God would still exist outside that stone, that would mean that the stone would be of a finite mass, which is false.
Therefore God would no longer exist while the stone which He cannot lift exists. So there would be no one left to lift that stone.

That proves that the paradox does not take place.