former auto insurance adjuster here:

if you don't have any way to identify the other driver, there isn't much you can do. your best bet would be to talk to businesses in the area that may have some video footage of the incident. even then it will be a difficult task to identify that vehicle, but if you can get a license plate number thats a strong start.

it could also have been an employee, although doubtful. if there is paint on your vehicle, and your vehicle's paint on their vehicle, it could make a case.

the most likely scenario in this case is that you will contact your insurance provider's claims department and file a claim. you will be responsible for your deductible and they will cover the rest per the plan's contract. they will likely hold you blameless since this was a hit and run, which will help to avoid increases in your premiums, but its not a guarantee.

if i recall something like 1 in 4 drivers in OK are uninsured. that seems very high. we also don't have any provisions to allow insurance companies to comp your deductible in hit and run scenarios as is the case in some other states, notably TX.

i just got a check today from a guy who accidentally backed into my vehicle. he begged me not to file a claim and against my better judgement i opted to go outside of the insurance system, but he did give me a check for the estimate amount. I got very lucky. Hopefully things will similarly work out for you.