Sorry to hear about your luck.

Do you have a personal vehicle with insurance? If so, you might well have that coverage in effect at least partially (loss of use for example is commonly excluded). How bad was the damage? If you whacked a guardrail that sounds moderately expensive. If you’re paying out of pocket I suppose it doesn’t matter but I think just about every insurer will want a police report. Double check your credit card to see if you have some coverage. Also, was this work related? Most larger employers have coverage for this. You may have not known any better and I agree it can be really stupid but many groups will look at you funny for not having a police report unless minor damage (they assume you were DUI). Now if this was in some snowstorm then they may just look at weather report at time of reported incident and be fine as well.

It it will probably take a few weeks for Avis to contact/bill as they’l need to do an estimate. How ever much you think the dollar amount in damage was caused, be prepared for a bill that’s double that.