I think solutions depend on the countertop material and edge. For example, I think it's possible that 3cm material may not require any additional support (confirm that). I'd be surprised if some additional support wasn't indicated for 2cm material though, and steel is typically the best solution for cases like this. If you conclude that additional support is needed, then you need to consider how much space you have under the counter for a structural member. For example, a 1.25" square steel tube spanning the gap would work well if there's space for it, and this material is typically available at the local hardware store. If you go this route, be sure to clean the top of it well and maybe buff it a bit before countertop installation so that the countertop adhesive bonds to it because steel reinforcements like this are 5-10x stronger when the ends are fixed rather than floating.

I am a fabricator.

3CM would not require a support unless it was a particularly weak stone. If you really wanted the underside unobstructed you could have the underside of the stone relieved by 1/4 or 3/8" and then inlay 1/4 or 3/8" structural supports that spanned the opening and projected over the adjacent cabinets. Grinding out the cavities for the inlaid support is relatively easy if the fabricator has a CNC or even a good bridge saw.

I personally wouldn't do it without a ledger in back and some steel in front. But then I'm a pessimist and would expect it would be my luck that a weak fissure was right over the space and that would be where some idjut would want to sit at the next party.

Have your fabricator epoxy 4 full length stainless steel rods into the underside of the stone. Jump up and down on it if you like, it's never going to break.