Finish a laser engraved piece of wood
Use a sanding block (ie, do not hand sand with your fingers) which will prevent the sandpaper from pressing into the grooves.

1 mm is huge, for anything reasonably described as fine sandpaper and not applied with excess enthusiasm.

But, as is always the case, testing your complete proposed finishing process on a suitable piece of (in this case) laser-engraved scrap would be the best bet.