The old shower pan was placed directly upon the foundation. The old shower had a center drain and in the foundation there is a diamond shaped cutout for the drain trap to pass through (see image). The tub needs a bed to support its entire base which needs to be about four inches higher than the foundation. My question is, should I fill in the hole in the foundation where the drain trap is with the bedding material (mortar is recommended) or does the hole need to stay there for the drain trap?

I think if you want to raise the tub 4" build a 4' x 8' deck with 2 x 4s

When building deck put in two or three cross pieces to support the tub

Make it so you have a step area out side the tub so it isn't that tall to

step out of tub... If you do it right you won't have to move the drain

Cover deck with 3/4" plywood and place tub on top of it

There may be other answers -- you have to decide how to do it