That's not what I meant. I meant if time is not fundamental, then there must be a time-free formulation of the laws of physics and also the universe itself must fundamentally work without time. I can somewhat - but certainly not fully - wrap my head around a time-free formulation of physics for specific situations and recovering time from that as an emergent phenomenon. But thinking about the universe as fundamentally time-free just breaks my brain, I can not overcome the thinking that change happens over time while the truth is probably closer to time emerges from change, roughly speaking. I guess because we are so used to reductionism, thinking about things as the sum of their parts and how they work, we or at least I struggle when something is not decomposable. But time seems to fall into this category - if there is a single isolated particle, then there is no time, it only shows up once there is a composite system and relations between its parts can change.

The term "Arrow of Time" is something that might be relevant to what you're considering; which is a somewhat unsolved problem but generally thought to be caused as a statistical consequence of there being a very low entropy state in the past.

This is a different problem - the laws of physics when formulated in the usual way with a time dimension are mostly symmetric or reversible, i.e. there is no obvious difference between past and future. As you said, one of the proposed solutions is a low entropy initial state that can break this symmetry and help to explain the perceived difference between past and future.