There is a more difficult conversation about entropy that might address the "flowing" of time or the experience of it as sequential. I'm not super qualified to talk about that particular issue though.

My basic understanding is that time and entropy together (with the initial conditions of the universe, hot with low entropy) create a physical universe that includes causality. Then, consciousness relies on causality because it's about recieving information, processing that info, and acting. Then, we can consider natural selection, and think about how our consciousness appeared in this world in the first place.

Sorry that's not rigorous. I don't have a full answer. You bring up some good points. Still, I think entropy is related to the answer about time flow, and I think that how we experience time is a result of both its physical properties and our brains' physical properties.

Edit: the entropy, time, and big bang stuff is a Cosmology topic, btw, for whoever's into this sort of thing