If you think it would be a worthwhile use of your time given that the amount of damages is supposedly $650, and you'll likely have to pay a filing fee to bring an action, you probably could sue the other driver in a small claims court.
You'll each be able to tell your side of the story, and show whatever other evidence you have (BTW in some locations a mere estimate from a repair shop -- instead of a paid bill for completed repairs -- won't cut it) to the trier of fact (possibly a judge but in many jurisdictions a volunteer attorney who the court designates to serve) and see what happens. If you win, and the other driver does not voluntarily pay on the spot, you'd then have to go about collecting the judgment, which is not always easy.
You'll each be able to tell your side of the story, and show whatever other evidence you have (BTW in some locations a mere estimate from a repair shop -- instead of a paid bill for completed repairs -- won't cut it) to the trier of fact (possibly a judge but in many jurisdictions a volunteer attorney who the court designates to serve) and see what happens. If you win, and the other driver does not voluntarily pay on the spot, you'd then have to go about collecting the judgment, which is not always easy.