You can still sue the at-fault driver or any other liable party. However, it may be challenging to identify and locate the at-fault driver in a hit-and-run case. This explains why, as advised earlier, it is important to report the accident to the police immediately and gather as much evidence as possible to help identify the driver.
Keep in mind that even if the driver cannot be identified, you may still be able to recover damages through other means, such as other forms of insurance you may have purchased. For instance, if you got hit while driving a rental car, the rental car insurance company may be able to compensate you, but only if you have an aggressive attorney to help you fight back.