How do I know if I have engine damage after overheating

Step one is to trust your service provider. Allow them to properly inspect vehicle. Afterwards If you don't agree with findings/pricing. Seek a second opinion. Also Keep in mind if the present repair facility quote is high it might have to do to excessive overheating. I am almost certain the repair facility is NOT a non for profit organization. How long was vehicle driven for? Where was the temperature gauge at during breakdown? Why did belt break? (lack of maintenance?) Or did something within the belt circuit seize? Keep in mind that today vehicles have many plastic components such as intake manifold, Engine Thermostat housings, radiator hose connectors etc... That can NOT withstand engine overheating/meltdown conditions. Too many variables to know at present. Update your question once you get Service station findings. Good luck.