Darwinian aliens are distinctly possible, if unlikely, within what we currently know, but the infinite aliens would require a LOT of proof... Along the lines of us tracing back the big bang and finding out the explosion spelled "LoL. We've been here forever. Bet you can't read this for another fourteen billion years". The more extraordinary the claim, the more extraordinary the required proof... And infinite aliens are infinitely more extraordinary than Darwinian ones...
EDIT: I'm sure there's a more reasonable proof they would be able to provide... That's just all I could think of off the top of my head.
EDIT2: This seems like the same argument, and basically is. The idea is that a creature that has always been is so far out of the realm of known science that it cannot be reasonably conjectured at this time with any scientific merit. (Though they always make for interesting thought experiments)