No, you should almost certainly
not buy a Pontiac Grand Am with 277,000 miles on it. Cars of that age and mileage are extremely likely to have significant mechanical problems that will be expensive to repair. Even if it seems to run fine now, major components like the engine, transmission, suspension, and electrical systems are nearing (or beyond) the end of their lifespan. You're almost guaranteed to face substantial repair bills very soon after purchase.
Unless you're a skilled mechanic with access to cheap parts, the cost of ownership will likely far outweigh the purchase price. The car is very likely to be unreliable, leave you stranded, and cost more in repairs than it's worth. It's a huge risk. Consider a much newer and lower-mileage vehicle instead.
