So yes, a universe sized lifeform could not have evolved randomly since the big bang, but you can only be confident about that if you assume that nothing exists outside the spacetime bubble we call the universe.
It's fun to kick around crazy ideas on Saturday afternoon. It could be anything. Sadly, there's no way i'll ever know. But the idle speculation is still amusing.
Does it really make sense to talk about it as being a single organism? How could it do anything in a coordinated way?
Or how about an organism that grows at say 10m in diameter per year, but signals across its body only propagate at 1cm per year? Again, how can it be considered to be functioning as a discrete organism? Surely if such a being evolved, its parts would perforce do so independently of each other? There could be no cross-organism coordination. It would have to disintegrate or devolve into local functional or operational units if it were to do anything effective at all.
Ae could be in it's stomach, where processes slow down the speed of light by a factor of trillions so that we are easier to digest.
None of these are testable hypothesese of course. But one day they may be testable.