What you are describing is infinity. For infinite time, this cycle has existed.
That concept is easy to say, but very difficult to mentally accept. We’re too accustomed to thinking of time linearly since we’ve never had examples to the contrary.
For starters, linear things can be infinite too (e.g. integers). Being cyclic and being infinite are separate.
Second, I do not know if time is finite or not, but i do know it lasts longer than i do, and anything that does is essentially infinite from my perspective.
Is a time crystal a counter example? Guess its not something we would normally encounter anyways.
Also,i feel there are no satisfactory answers here. See also https://en.m.wikipedia.org/wiki/Unmoved_mover