Interesting thread, though I'll admit footsteps on stairs is one of those phenomena I approach with considerable scepticism before jumping to conclusions.
Before attributing it to anything paranormal, it's worth ruling out the mundane explanations methodically. Thermal expansion in older timber staircases is remarkably convincing - particularly in Victorian and Edwardian properties here in the UK. As temperatures drop overnight, wooden treads contract and produce sequential creaking sounds that genuinely do travel up a staircase in a plausible footstep pattern. I've documented this extensively in my own Sussex property using a Zoom H5 recorder and the timestamps correlate almost perfectly with the 2-4am temperature dip.
That said, once you've eliminated the structural explanations, the residual cases become genuinely fascinating. Repetitive auditory phenomena - particularly those following consistent routes through a building - are among the more compelling categories in the literature. There's a strong argument that certain environments retain some kind of imprint of repeated human activity, which manifests acoustically under the right conditions.
What would help enormously here is more detail from the OP:
Age and construction of the property?, Was it a one-off or has it happened before?, Any correlation with weather or temperature changes?, Did anyone else in the household hear it simultaneously?
Corroborated simultaneous witness accounts are really where things get interesting. A single person hearing something ambiguous at 3am is easily dismissed. Two people waking independently and comparing notes immediately afterwards - that's a different conversation entirely.
Would encourage anyone with recurring experiences to start keeping a log. Patterns only emerge over time.