If you claim that God is eternal, you're making an admission that it is possible for something to exist without a cause, that is, something either responsible for its own existence or simply neverending. If you can apply that trait to God, why not the universe instead and just simplify the question??
How's life? Are you still pursuing engineering?
Regarding your rhetorical question, if we consider matter/energy as eternal, then there can be no creation or destruction of matter/energy (by definition of matter/energy as being eternal). This contradicts the quantum theoretical concept of 'virtual particles' as the actual creation/destruction of matter/energy (i.e., due to the uncertainty principle). I guess it's possible to consider virtual particles as an abstraction (not a real aspect of the universe), however there is a deeper problem with an eternal universe.
With respect to God, one can argue that causality in the universe is a consequence of God (i.e., God as 'truth', God as 'logic', God as 'mathematical order', etc). In case of a materially world as primary, causality is a result of material processes, and therefore there are no real causes in the world. That's problematical since science gives the impression at least that there are genuine causes to things. Anyway, I think the premise that the universe is eternal without there being a 'God' is more problematical than the universe being infinite or finite as a result of God's existence.