The 747 argument makes at least 1 major flaw, making it a horrible comeback to the design argument.
1.God is outside of linear time. In other words the argument "who designed God?" is nonsensical, because it is literally asking "Who created the being that was not created?"
God does not see time one day at a time. God knows all reality, from Creation on forever, in an eternal instant. He has no tomorrow, or yesterday, only "NOW". And His "NOW" encompasses all reality.
Therefore unlike the universe, God does not require a creator, because He is eternal. Not eternal in the sense that He has always existed (in which case we could well ask "who created God", because we know all things in time require beginnings), but rather eternal in the sense that He is not in linear time at all, and therefore asking "who created God" is nonsensical, because since He is outside of time He needs no creator. Aquinas was teaching eternity before Einstein was born.
As to your question about the idea of God being nonsensical, it is not. The reason people think Theology is stupid is because its almost always taught either by dumb people who don't understand it, or smart people who don't believe it.
It is a leap in logic to think that because many Christians are stupid, that Christianity is false.