You need to determine the depth needed for not only the trap but the height from the trap inlet to the desired height of the floor when the drain is added. The drain itself is 3-15/16" tall.
https://sccpublic.s3-external-1.amazonaws.com/sys-master/images/hc8/hd7/9000342159390/Shower System Data Sheet.pdf page 13. So depending on where the inlet to the p-trap is and the thickness of the foam pan, you may need to raise the floor some if the line is higher than desired. On their system, you can do that with a sheet of foam underneath the pan that you laminate in place with thinset. Make sure that the floor is both flat AND level before installing anything and pay VERY careful attention to getting the trap riser perfectly plumb. I think that I'd glue in the riser (you can always cut it off to the needed height afterwards, if required), place something over the top of it, put a bubble level on it, and then glue the trap into the trap arm. Hold the whole thing to keep the bubble level perfectly centered while the cement's solvent evaporates so that it doesn't move. Dry fitting just doesn't really work with PVC, so you have to measure carefully. There's very little horizontal leeway in the placement of the drain in the shower pan depression...maybe all of 1/4-3/8", if that. There's almost no vertical leeway. When calculating heights, keep in mind that there will be some thinset under both the shower tray and then on the drain itself. If you use the recommended trowel size, it should be less than 1/8" of thinset. If the floor is a little rough, you might need to go up slightly in trowel notch size to ensure full coverage.
If the pipe inlet does not have enough depth to attach a trap, then yes, you'll need to cut out the plastic box.