The floor inside your kitchen sink cabinet is highly susceptible to damage caused by an occasional water leak or condensation dripping from sweaty pipes.
Protect the floor with a single piece of vinyl sheet flooring. Cut the flooring to fit tightly inside the cabinet. Remove the flooring, spread flooring adhesive around the perimeter of the cabinet floor, then press the vinyl flooring into place.
Finally, caulk around the perimeter of the vinyl flooring to create a watertight seal inside the cabinet.