Here's the thing, a FB marketplace listing is free to renew forever, so if they don't need the money quickly they can just ignore all of the low ball offers. You need to get the invested, make them feel like it'd be a waste to let the sale slip away. Message them with some questions, then once they answer wait a couple of days and hit them with some more. Then go see the car in person, test drive it if they'll let you, and most importantly build rapport. If it's an enthusiast car ask them why they bought it and let them talk. Find out why they are selling, what they want to do with the money, etc. Make them like you.

Then hit them with a reasonable number, but below your max. If they still aren't willing to move on the price then you politely thank them, say you'll think about it and leave. If they move a bit I'd consider the possibility you can make a deal to still be alive, try again in a week or so with a higher offer, but if they don't move at all then you are likely SOL. The car need a couple of months to sit on the market, let them keep paying to maintain and insure it.

You can show a comp or two, but DO NOT USE KBB for an enthusiast car, they never get it right. I'm currently selling an enthusiast car, a 2000's Porsche that regularly sells for $15-20k, but the KBB value is $8k. If someone mentions KBB I ignore them, they don't know the market. I'm willing to go below market, I'm not willing to take a dumb number based entirely on what a dealer would give me as trade in value. A better way, that is actually a good idea regardless is finding a local mechanic familiar with that specific brand or model or car and pay for a pre purchase inspection if the owner will let you. If it comes back perfectly clean then it won't help you at all, but odd's are it won't. If the local dealership is willing to do the PPI that's even better, they will throw the book at the car and you'll get back a repair bill that exceeds the value of the car even on a seemingly perfectly fine example.