You should be able to lower the stove--don't ask me how, but we went through this last week, and my husband had to level the stove so I know it can be done.

First, is it a cooktop (that's what the second picture appears to be) or is is it a slide in range? Do you have some pics from a bit of a distance to give a perspective on the situation?

If it's a cooktop, the cutout is too small and needs to be enlarged so it can sit down in the hole. That's easy. Just call the granite fabricator.

If it's a slide in range, were the cabinets already in place and then flooring was added afterwards? There isn't a good fix for that issue. You can try taking off the feet, but that makes it almost impossible to get the range in and out of it's cubby. You can remove the flooring in the range alcove, but again, if you ever get it in there, it's not gonna come out very easily. You can have the granite fabricator cut thin strips and laminate it to the counter around the range, but that can be awkward for sliding pans off. It's probably the best solution in many respects though.

Can you place something underneath the island to lift it up

Thanks everyone. Per your ideas... We can't lift the counter or lower the stove, and the stove is a slide in model. I'm thinking that there must be a quality product available to fill the gap between the stove and counter- primarily to avoid having spills and crumbs fall in this space. I'll call a granite fabricator, and see if they make something to address this... We appreciate the ideas!
Btw, I loaded other pix of the stove

I have the same issue. I had to slide out the stove and lower it using the leveling legs so that it would be flush with the counter.

We just bought a slide in to replace our old one. We had to buy one that had a lip around the range top that came at least 1/2 inch over the granite. Ours (Samsung) came with black spacer bar for the back edge, which we did not need. I wish the sales person could have addressed that with you. Call the manufacturer to see if they have a solution. Google luck

Good luck, spellcheck!

Did you ever find a solution. New jenn air design creates same issue