I've heard experts claim that there are models that show that an infinite past universe is possible, is that so?
Yes, there are other models, BUT your subject heading says “good evidence”.
So the only real evidence we really have points to the Expanding Universe Model, which is what loosely called from the 1920s, but was later more popularly referred to as the “Big Bang theory” since 1949.
Since the late 1990s, the Big Bang theory was expanded to include the Dark Energy denoted by Greek letter lambda and Cold Dark Matter (CDM), so the new name for the Big Bang theory is “ΛCDM model” (Lambda-CDM model).
Anyway,
@epronovost is correct, the Observable Universe points to universe being UNDER 14 billion years old.
Ther other models but they are not science yet, because there are no good evidence for these alternative models. The only reasons why these models are not thrown out as garbages, is because these models provide mathematical solutions - meaning equations - that are still theoretically possible, but without scientific evidence.
Equations are good and useful tools in physics, but maths are not evidence.
Science needs “evidence”, not equations, evidence to test and either verify or refute any model.
Those “models” you talked about are only “proposed” models, not scientific models.
Anyway, there are no “good evidence” that points to eternal universe. Actually there are no evidence at all.