I would say it seems like both space and time are emergent rather than fundamental. The clue to this is that time irreversability is about state spaces, probabilities, rather than geometry.
The fundamental laws are all time reversible (except deep inelastic scattering, involving the weak nuclear force). But quantum-states that start out pure, tend to become mixed; information spreads out. This asymmetry, directionality, is a type of pattern, that our minds need to perceive in one direction, because that represents information reaching us - moving differently through the state space would see information do the opposite of spreading out, which we would perceive as time going backwards; ie the reverse of perception, ie. we can't percieve it.
Looking at cyclical cosmologies like say Conformal Cyclic Cosmology, we can see this quality of time as linking together a LOT more states than if there was 'just' perfect symmetry.
I went into more detail in a recent answer here Why is the universe governed by very few laws of high generality instead of lots of particular ones?
To summarise in relation to your question:
In the beginning there was nothing, but being nothing it couldn't be certain about itself, and so the universe began. Gigantic state spaces that we can understand using just geometry, like E8, suggest our universe is something like a fracture plane in the state space of all possible universe-timelines, where the neat smoothness got 'caught' at an essentially random point. The anthropic principle requires to be in a fracture plane with certain properties, to be here to puzzle ourselves about it.