Pull the ledge and laminate a built-up edge to the bottom to lip over the gap.

have your tiles been grouted yet it doesn't look it.

"have your tiles been grouted yet it doesn't look it."

That area would not get grout, it would be caulked. Joseph's idea would be the way to solve this issue at this point.

I personally like the reveal and the larger gap with a change in materials. If you could figure out how to keep that shadow line, I would, and recess the caulk slightly

They haven’t been grouted yet but the ledge has tile on top of it so tile would have to be pulled off. I would worry about damaging the waterproofing at that point, right?

Pump the gap full of color matched silicone and forget about it. Ain't nobody lookin' there anyway but the cleaning lady.