"Any ideas !?"

Yes. Retrofit an apron front sink. Stain is gone forever and no damage to countertops, cabinets, and backsplash:

Interesting idea. Would installing a farmhouse sink also involve removing the countertop? Or could you keep it in place?

the cabinets are wider than the sink so we would have to retrofit the cabinets as well?

"Would installing a farmhouse sink also involve removing the countertop?"

No. The tops aren't removed and the risk of damage is very minimal.

"The cabinets are wider than the sink so we would have to retrofit the cabinets as well?"

No. Your cabinet appears to be a 36" (or larger) which is perfect for a retrofitted short apron sink.

Please measure from the cabinet front to deepest part of the existing sink cut out and post. I can tell you which sinks you can choose from with that information.

Your job would be more like these instead of the one linked above.

Not sure what you mean... cabinet front to back of sink is about 19.25 inches. Cabinet from to sink is about 21 inches. width of cabinets are about 41.5 inches.

Unless you have matching material (42" x 6") and don't mind trading a single seam under the faucet for a seam at each end of the sink, that's the only way a stock Kohler 3943 or a stock Elkay Quartz Luxe is going to work. If you don't have additional material, or the extra seams bother you, you're going to have to go with a custom sink. With a 42" cabinet, that's not a bad idea.

assuming we have material and don’t mind two seems, how much would this project cost in total?

Your fabricator or you have to be comfortable with about a $3,500.00 budget; sink and plumbing included.

If they had 1 broken tile on the floor, would you have recommended to replace the subfloor?

Michael, if you haven't replaced the sink yet, a local stone restoration company to address the stain instead of a full kitchen remodel...

Tile and Stone Pro:

Please read and comprehend all of the previous posts before responding. Had you done so, you would have read that the OP's " marble guy tried getting out the stain using a poultice but it didn’t work. He offered to replace the section of countertop..."

This is the metaphorical equivalent of attempting to replace 1 tile. It didn't work.

Furthermore, the OP is " worried removing the countertop will damage the brand new cabinets and backsplash."

My suggestion to install an apron front sink eliminates this worry and could hardly be characterized as a "full kitchen remodel".

"So we are looking for a way to lighten this stain to make it less noticeable. Any ideas !?"

Removing the offending stain lightens it completely and makes it completely unnoticeable.

The correct materials mix in the poultice may remove the stain. I would try again.

Also, chip the stain out, glue in pieces of shredded marble. Hone. - Works for sure!

"Also, chip the stain out, glue in pieces of shredded marble. Hone. - Works for sure!"

That's hillbilly. For sure.

Not if you know what you're doing. I have done it and EVERY other stone restoration company should be able to do it.