You don't only have a gap at the top. Imo, the misalignment of the door to its neighbor is not correct. The upper panel doesn't match a drawer front for width. I'd review the pullout cabinet choice and installation instructions for the different options. I cannot see the cabinet manufacturer accepting this outcome for their product and your use.

If you continue forward with this you need apiece of wood to fill the gap painted the same color as your cabinets.

If you pull your new cabinet out you can put 1/2 inch plywood the size of the base under it to bring it up. Kick plate can cover the edge of the plywood and you can get a door that matches your existing cabinets from Barker Cabinets if you want.

Thank you for your response. I did saved the trim, but the thing about pulling out the cabinet out and putting the piece of plywood is that it won’t fit back in. I don’t know if you can see it in the picture but the laminate floor is 1/2 inch higher and there’s a dip into the space. The previous owners put new flooring but didn’t replace cabinets or countertops. I do plan to remodel the entire kitchen in the future. In the meantime it’s an eyesore. Here’s what it used to look like with the old broken trash compactor.

Remove the toe kick off your new cabinet. Now you can reach under and use shims to raise it up to the correct height. Reinstall the toe kick.

What if you filled the area under the cabinet with plywood so that it's flush with the flooring. You would then be able to push the cabinet back and it might be just the right height to fill the gap?