50 amp outlet Use existing or move it?

As George stated it only has to be accessible.

Since doing a remodel I would look to see the direction of the feed. It may be possible to move the receptacle to the center of the opening or possibly even to the edge and not have to cut the cabinet at all.

I usually provide small service loops of a few inches this could allow the receptacle to be moved from 1 stud to another or if the direction of feed allows to the center of the opening. Both of these options only cost a little sheetrock and may provide a professional look over a cut hole in a cabinet.

Have I ever cut a cabinet do do something like this as a professional? Yes as it saved hundreds compared to replacing the feeder, receptacle and a permit plus the delay for inspections.

If the receptacle can not be moved over and you cut or notch out the cabinet base I would suggest making a box inside the cabinet so when looking in the hole is not visible. The receptacle box must still be accessible without damaging the finish. I use Velcro adhesive strips to hold things like this in place but screws are ok also. It must be made to be removable and the finish can not be damaged when opening. This will provide a quasi professional look compared to just a hole.