Cats are naturally curious, affectionate and territorial. If you have a raucous household and other pets, under the DW is not an ideal place for him to be.
However, dragging him out of there will be a trick.
If there is a way to keep other pets out of the kitchen and keep things quieter than usual to not scare him, it would be better to not traumatize him by dragging him out of there, which you might be unable to do.
I suggest: definately don’t run the DW, try to keep that room calm and quiet, put a bowl of food and another of water just outside the DW. Also a catbox, I know, in the kitchen is gross, it’s only temporary. Basically you want to have everything he needs, right there where he can see and smell it, close to his hides hole.
He will eventually start to come out to eat, eliminate and eventually explore. This is exactly what I would suggest if he did the normal behavior of hide under a bed or dresser or in a closet. Try to just leave him to himself and let him acclimate.
If it were me, I’d keep that kitchen SUPER quiet and also drag in a pillow and blanket and *I* would lie on the floor 6 or 8 feet from the dishwasher and read or engage in some other quiet activity where he can see me but not so close he would feel threatened.
When he does come out, you can talk to him softly (you can also do that now) but don’t chase or grab him.
And get a dishwasher toe kick so you can close off that particular spot as soon as he comes out.