That’s a lot of money to spend on a car from a private party with no warranty. But the distance really has nothing to do with that issue. You’d be taking the same chance buying a used car locally from a private party in that it could blow the engine the next day leaving you with nothing.
If you decide to do it I would tell the seller the sale is conditional on you taking the car to a local mechanic and them saying it’s 100%. You’ll find a lot more putting a car up on a lift than doing a quick test drive and trying to look under it in the parking lot. The mechanic will be looking at it with an unbiased eye, compared to you looking at it while in the back of your mind you’re thinking how much you want the car, and how you just spent all this time/money getting there to buy it.