Think of it this way: We don't have any way of measuring time that doesn't also involve space. Whether it's pendulums, or atoms vibrating, or photons bouncing around, any way we measure time is linked to (and relative to) whatever space is around it. If space is being deformed by a large mass being there, time will be affected (slowed down). Some theories of time say that what we think of as 'time' is really just a byproduct of space.

So if space didn't exist (in any meaningful way that we would understand today) before the big bang, time couldn't exist either.

That's like trying to imagine what being dead "is like" for materialist atheists. If you don't believe in an afterlife, then your consciousness simply ceases. There is no experience of being dead.