How did God come into being, existence?

God did not come into existence.  He has always been in existence.  The Bible says that He has always existed:  " . . . even from everlasting to everlasting, you are God" (Psalm 90:2); and, "Your throne is established from of old; you are from everlasting" (Psalm 93:2).  Quite simply, God has no beginning and no end.  So, when we ask how did God come into being, the answer is that he did not.  He always was.

But let's explore this little further.  If God did come into being, then we would have to ask what it was that brought him into existence.  Whatever that was, it would have to be greater than God and the question would go back yet another step because we would have to ask what brought that into existence, and so on and so on.  There would never be a beginning.  Think about it this way with a thought experiment....

Let's say there is an infinitely long line of dominoes, where one domino is falling into the next and so on.  This represents one thing causing another thing to happen.  The question we need to ask is, "Can the dominoes have been falling, one after another, forever?"  The answer is no. 

If we were to travel back along the line of dominoes looking for where it all began, we would never be able to get to the first one.  That's because with an infinitely long line of dominoes, where each one has been falling one after another forever, we would never be able to get to the first domino because there would not be a first domino that started it all.  But the problem is that if there is no first domino that started each one falling, there can't be a second domino that is falling, nor a third, nor a fourth, and so on.  It just does not make sense.

So it is best to accept the idea that God has always been, just as the Bible says.