Do you mean timewise or distancewise ?
Assuming distancewise, the only explanation that makes sense (of a sort) to me is the concept of curved space. That if you lived forever and moved faster than light, and set off in a straight line (however you work that out) that you'd eventually end up back where you started (however you managed to recognise it). So space is finite but doesn't end. Any experimental data that suggests space is flat implies to me we simply don't have the ability to note how small the curvature is, nor how vast the universe is.
As you imply, any attempt at a different explanation makes it very difficult to come up with what sounds a reasonable answer.