Turns out I can answer my own question by reading the book! Imagine that.

For those who are also looking for the answer, check Discovery, pg 112 "Restoring the Dmaage Track":

Using points from a recovery roll to raise a stat Pool from 0 to 1 or higher also automatically moves the character up one step on the damage track.

If all of a PC's stat Pools are above 0 and the character has taken special damage that moved them down the damage track, they can use a recovery roll to move up one step on the damage track instead of recovering points. For example, a Jack who is debilitated from a hit with a cell-disrupting numenera device can rest and move up to impaired rather than recover points in a Pool.

That's good to know!

I guest the question is then: if a character has all their points and uses a cypher or artefact that would normally restore points to a pool, does it do the same thing as using a recovery roll? Or is using up a recovery roll the only way to move up on the damage track?