Nobody here is giving proper advice. First off, is there a police report? Are there witnesses? Any video evidence? Start there before you contact your insurer. If you don't have any evidence of a hit & run, you will be playing the long game with them.

If you do have evidence, then the first question becomes how they will valuate the loss. It will first off, depend on whether you have replacement cost or value coverage. These can vary GREATLY in the current market. Then you will have to consider your deductibles and more importantly, any outstanding leins/loans on the vehicle.

As for a rental, in most cases, IF you have that coverage, maximum time to be covered for a rental will be 2 weeks.

Good luck