[Mike Shebel]

Possibly an easy solution.
If the front legs are already sitting on top of the tile, open the dishwasher door fully, push down on the outer edge of the dishwasher door, which will cause the dishwasher to pivot on the front legs and raise the back of the dishwasher up.
At the same time, pull the dishwasher forward.
The back of the dishwasher should have more clearance than the front of the dishwasher and should slide out of the opening.

[Topspinmo]

Originally Posted by Meyerro

And have the tile installed all the way to the back

That may not work cause no room under counter for extra 3/4 of inch height. Could also be problem when replacing old refrigerators which I ran into with 3/4 inch tile.