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.
