Sure. Dig it out.

You should have a gasketed escutcheon anyway. Plumber's putty can stain natural stone.

If there's nothing wrong with the hoses, but they're too short, you can add extensions. If there is a problem with the hoses, that material can likely be pried out in small chunks with a screwdriver, but the hose ends you find up inside there may not be detachable. I'd opt for a new faucet instead of trying to fix that.