Big bang theory
Flat universe theory
I believe in the universe is probably finite. Yet, that does depend on how you define the universe exactly; is it just the space made by the big bang, or is it also include the space that the big bang blew up in. If its the first then yes it is finite, but as for the second I would say infinite.
CMBR, Expansion of galaxies, dark energy, abundance of primordial elements, nucleosynthesis
Even in flat universe big bang happened.