First, if your island's total depth, including the counter, is 39" and you have a decorative door or end panel on the backs of the cabinets, then your seating overhang will be 12.5" deep, not 15". There will be approx 1.5" of overhang in the front of the island over the cabinets (to protect the cabinets, doors/drawer bases, and insides from spills & drips). A decorative door or end panel installed will take approx 1".

So: 39" - 1.5" cabinet overhang - 24"D cabinets - 1" decorative door/end panel = 12.5" left for seating overhang (no decorative door/end panel, then 13.5" seating overhang).

Islands with the recommended minimum 15" seating overhang are 41.5" deep to account for the front counter overhang & the decorative door/end panel: 1.5" cab overhang + 24"D cabs + 1" decorative door/end panel + 15" seating overhang = 41.5" (Without the decorative door/end panel, the depth would be 40.5".)

Per Joseph Corlett: You can cantilever Ceasarstone less than 16" without additional support. It's one of the advantages quartz has over natural stone.

I don't know if you need support for a 54-inch wide island, though. I suspect you probably do and I would probably recommend every 30" or so, which, IIRC, is what is recommended for natural stone.

Are you installing the counter? The fabricator should be figuring this in to their install. Are you talking decorative suppport or integrated support?

I agree with DETAILS. Whomever is installing your new countertop should be discussing with you how to support the overhang.

The island needs to be fastened to the subfloor, have electrical outlets, and have counter support. That means that the cabinet part of it has to be designed correctly, and robustly enough, for all of that. It all starts with your kitchen designer, the cabinet specs, and the design documents that communicate all of that to your GC and installer. If you are the designer and GC, you have a lot of boning up on codes and cabinet structural details to do here to make that safe and usable as intended.