The Big Bounce[1] hypothesis is a model that "suggests that we could be living at any point in an infinite sequence of universes". So while our current universe may not be infinite there may be some yet undiscovered infinite/eternal natural process that gives rise to universes.
Olber's Paradox[2] and the inability to reconcile it with our current astronomical observations seems to disprove that our current universe is itself infinite.
Olber's Paradox[2] and the inability to reconcile it with our current astronomical observations seems to disprove that our current universe is itself infinite.
[1] https://en.wikipedia.org/wiki/Big_Bounce
[2] https://en.wikipedia.org/wiki/Olbers%27_paradox