B Is an infinite universe compatible with cyclic models?

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Cyclic models, such as the Big Bounce, propose alternating periods of expansion and contraction, leading to a series of Big Bangs. An infinite universe raises challenges, as it would necessitate an infinite amount of matter to contract into a singularity, which appears implausible. The Big Bounce suggests that quantum phenomena trigger the bounce while maintaining finite density. This mechanism could theoretically occur throughout an infinite universe, similar to how a Big Bang might arise. The compatibility of infinite universes with cyclic models remains a complex topic in cosmology.
TheHeraclitus
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If space is flat and infinite are cyclic models possible? The answer seems intuitively no but I wonder if it's correct.
Cyclic models for reference.
I will take simple Big Bounce as an example of what I have in mind.
In Big Bounce there periods of expansion and periods of contraction which result in a never-ending series of Big Bangs. However if Universe is infinite in extent this would require infinite amount of matter would have to contract into one point but that seems impossible.
 
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The big bounce implies that quantum things cause the bounce while the universe still has finite density. That could happen everywhere in a spacially infinite universe - in the same way that a big bang can.
 
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