It is unknown by the present evidence of physics and cosmology whether our physical existence is finite and temporal or infinite and eternal.
Steady state universe was rejected long ago.
recycling? odd terminology. The models for a cyclic universe are still proposed by cosmologists based on the same knowledge other models are using including the various BB models and multiverse models.
More explanation available from this website.
From:
https://physicsworld.com/a/cyclic-universe-could-explain-cosmological-constant/
:
Cyclic universe could explain cosmological constant
Two theoretical physicists have developed a model that could explain why the cosmological constant takes the small, positive value that it does in today's universe. The value of the constant is responsible for the observed acceleration in the expansion of the universe. However, the new model, developed by Paul Steinhardt of Princeton University in the US and Neil Turok at Cambridge University in the UK, will be controversial. It requires that time existed before the Big Bang, assumes that the universe is older than the 14 billion years we think it is, and says that the universe regularly undergoes repeating "cycles" of big bangs and big crunches (
Sciencexpress 1126231).
Multiverse models of our physical existence are still possible, and based on models proposed by many physicists and cosmologists.
No offense, and in all humility, but neither of us mortal fallible humans can define nor describe the nature of God's relationship and Creation of our physical existence.