That's cool to hear others talk about time loop theory as I was very excited about the idea a while back!
First, I think it is likely that matter and energy have always existed. For a long time I believed there were a finite number of possibilities and therefore it was inevitable that the same scenario would eventually repeat itself, and the universe would stay in a loop. This would mean that I have existed an infinte number of times in the past, however, just as I am not aware of any past selves, neither were any of them and neither will any in the future. Therefore, they are more so copies of me in a diferent time than the same me that continues on in them.
However, I came to a realization a few years back that this is improbable that time would repeat itself. The reason is that the possible combinations of the universe are actually infinite and not finite. The reason is because of particle positions.
If 3 particles are each exactly 1 inch away from each other, then that is one possibilty. Consider that particle 2 moves .0000000000001 cm to the left. There are an infinite number of positions where particles can be, and so there are an infinte number of possibilities for the universe which map to the infinite amount of time. Therefore, it is possible that time loops, but it is unlikely.
However, something new I'm just now thinking is that perhaps the various gravitational pulls and other physical and chemical bonds makes it such that there are many positions that particles CANNOT take. Assuming a finite amount of matter and an eventually collapsing universe, there is a maximum radius of the universe, so these forces may enforce a finite number of positions that the finite number of particles can take, thus enforcing a finite number of possibilities and eventually leading to a repeat of identical events.