It's a pain but unfortunately it's pretty normal. Insurers look at your claim history over the last three years, and a fender bender in May is still super recent for them. You're flagged as "high-risk" right now, even if it was something minor. I've got a buddy who was in the same boat last year and had to wait several months before anyone would take him on. The thing is every insurer has their own criteria but generally the more recent the claim, the harder it is to get coverage.
There's no real official minimum timeframe, it depends on the insurers. Some will accept after 6 months, others want more like a year. What you can do is ask brokers directly how long it'll take for you instead of asking for a quote right away. Also check out insurers that specialize in drivers with recent claims, they actually exist and they're way more flexible than the big mainstream insurers. There's also the option of canceling your current policy if you still have it and find an insurer who accepts claims, even if the rates will obviously be higher.
My personal advice, based on what I've seen around me, is don't give up on the brokers and go back to them in two or three months. There's already some distance between May and now, and by September or October you'll have better odds. In the meantime, you could also check with your current insurer to see if they can keep you going until things calm down. Good luck, it's really frustrating but it should work out!