I see it mentioned as a fact that the universe is expanding. But I was thinking — how do we know the relative ratios of distance to time?

I don’t quite understand how this all works, but it seems like roughly we have an equation

distance = time * speed_of_light

and we know that the left side is growing relative to the right side. So we say “distance is getting larger”.

But why couldn’t we say that “time is getting smaller” or “the speed of light is getting slower”? Would those lead to the same experimental results that lead us to say that the universe is expanding?

I know this is all very hand-wavy, but how do we establish the absolute scales of any of these three quantities except by the other two? For example, if somehow distance was suddenly doubled but the speed of light was also doubled, would there be any observable difference?

Anyway I hope there’s an easy answer that someone can point me to.