While I won´t claim to be a Ph D. in mathematics, and not event a self proclaimed Platonist Philosopher as Dr. Hatcher
But I know what´s wrong with his proof.
While it doesn´t fall into the infinite regress, it falls into something similar.
Since the universe is a composite and can not be the cause of its components, there must be an external cause... ok.
By definition, if there is the universe and Dr. Hatcher´s G element, then there is a second metauniverse, containing G and our universe.
In that metauniverse, G can not be created by the metauniverse, since it´s a component of it. So there must be a G´ which created G.
If we decide, as he did, that G is self-created instead, why can´t every quark be self-created?
Why can´t there be just a dozen quarks, moving through time, and we see him many times because he crossed our position in time many times?
Are you willing to have a quark as your god? :-)