I use a waterproof stuff sack and an old toe strap and stuff the jacket into it and tie it under the saddle with the toe strap.
I don’t use my heaviest cycling jackets unless I plan to wear it the entire ride, if it seems it will warm up to a nice temperature I try to use a windbreaker and arm warmers and gut-out being cold for the first hour.

It’s the 30-40F zone where it looks like it might warm up only very slowly or might rain I need something warmer.