Yes, you can easily install a dishwasher in a space that has never had one.
I have had a portable, roll around, hook up to sink dishwasher for over, well, too many years to count. Recently, the Hubs and I installed a dishwasher, where none has ever been.
First, check you tube. Yes, tons of great videos on installing a dishwasher.
The before, my portable dishwasher and tools.
The purchase. Too good of a deal to pass up.
All doors and drawers take off the cabinets. Now let the cutting begin.
Cutting the hole.
Seriously the easy part. Hole cut. Follow the manufacturer's directions to hook up the hoses to the dishwasher.
Roll into space.
Push hoses to side. Hook to plumbing. Knock out garbage disposer connection, and hook hose to garbage disposal.
Do a loop (or hook to the airlock on top of sink)
Trust me this part was easy.
Ta Da!! yes, I will eventually put cabinets under sink, after we have some made. We have had a curtain for years under the sink.