Geico does not have an official time limit for filing a claim. The reason is that Geico cannot deny a claim based on late notice. To deny your claim, Geico would have to demonstrate that the delay was unjustified or unreasonable, or that the wait compromised the insurance company's ability to investigate the claim and reach reasonable settlements. Whether you decide to file a police report or not, it's always in your best interest to report a car accident involving another driver to your insurance company.
If you don't file a police report immediately after a car accident, at least be sure to exchange contact and insurance information with the other driver and photograph the damage to both vehicles, as well as the full scene of the accident. When filing a claim after an accident, insurers want to know who was at fault so they can decide what insurance will cover the damage. Even then, you may be able to talk to Geico representatives to ask them about returning the insurance payment and canceling the claim. Unlike Geico, insurers like State Farm and Allstate offer rideshare insurance promotions that you can add to a personal auto insurance policy.
If you're currently a Geico customer and want rideshare coverage, you can purchase a commercial policy separately or you can switch to a company that offers rideshare insurance.