I know what you mean..
I, myself, pointed that out to @firedragon in the start of this thread.
However, the idea that the universe has no beginning is not part of the argument.
If you think that the universe has no beginning, then it is not finite.
Good luck with that. Our lives here in this world are definitely finite.
I don't know whether the universe is infinite or not. Current evidence points to it being *spatially* infinite, but it is far from conclusive.
As for being temporally infinite, that is certainly a possibility, but again, we don't have evidence to say whether it is the case or not.