Vertical lift mechanism or push to open system for a cabinet lid?
I would consider two threaded rods in the back two corners that are rotated together and can drive up the lid.
They probaly need to be about 1/2” diameter as the lid length will cause a bending moment on the rods, unless you have extra sliding rods as well.
For initial testing a car wiper motor may be sufficiently slow - but that is easy to adjust when using toothed belts...