Hallett & Co.: Do you mean 1x4. surely not 1/4"

Renee: Just ask the company supplying the countertop. They do this all the time.

Does your quartz fabricator offer installation? I agree with the above advice that probably the safest solution is to screw blocking to the wall to support the quartz top, but you should get advice from your fabricator too.

I agree with tatts. I would not attempt to do anything, but let the company come out and do their job.

Sorry 1x4 (which is 3/4” by 3 1/2” because...)

In my area the counter installers won’t Install blocking, it’s the contractor or cabinet guys responsibility.

This is the cabinet installer's responsibility. I'd rip some 3/4" x 3/4" plywood and screw it to the studs. A 1x4 may block some dishwashers in the rear.

That isn’t on the counter installer to do. That is on the GC or cabinet installer. Who from the looks of things might not own a level. That’s the first issue to tackle.