Why is a universe that has always been in existence, cycling through different states, any more sensible than one that pops into existence only to ultimately fizzle out? Both require the presupposition of some kind of uncaused system. Gathering evidence pointing toward one or the other is key.
I do think that the Big Bang maps better to Western religious cosmogony (matter was created ex nihilo) and Big Bounce to philosophical materialism (matter is the fundamental substrate of the world), but that shouldn't bias a scientist against the Big Bang.
Curiously, Latter Day Saints (aka Mormons) have taught for over a century that essentially the Big Bang theory is incorrect and that matter has always existed and that when the Earth was created God simply "organized" existing matter rather than conjuring something out of nothing.
Putting aside their other beliefs I thought this was an interesting curiosity in this context.
Growing up LDS there was never any existential angst as I became more educated and there was never a need to overcome any cognitive dissonance as I learned evolution or cosmology- the baseline belief is a very sci-fi one of the first super-consciousness (God) taking upon itself the shaping of spiritual (dark matter?) and then physical matter and making pathways for other intelligences to master the same. No ex-nihilo involved.
Even if the LDS specific conceptions have all the details wrong, the overarching idea is completely plausible.