Is it possible to make a custom age caste? Or some other way of preventing Sims who are a certain number of days into the young adult category from getting pregnant with Story Progression?

Thanks.

I don't know for certain days, but I did a Caste for YA who are students not allowed to get pregnant, this works fine.
I think you could make non partner sims not allow to get pregnant, not marriaged ones etc.

The exact age of a sim within their current age stage is not reachable by the caste filters. The closest thing we have to this is the Near Elder Limit on pregnancies, but that of course that's only relative to a sim's expected Adult to Elder birthday. Sims should already be blocked from becoming pregnant if they are nearing any birthday, if aging is enabled, as a pregnant sim cannot age-up.

May I ask what is the goal is here more precisely?

I do one Sim day = 1 year in my age settings, so my YA age settings go from 19 to 45. I'd like it so Sims who are 40+ days old can't get pregnant with Story Progression.

Okay, I see now. That you can do. NRaas > SP > General Options > Options: Pregnancy > Near Elder Limit > (and set it to the difference between the age up to your elder stage and where you want your sims to no longer be fertile). I don't think this one will scale to occults who have longer life spans as a 41 day (year) old YA fairy for example would still be too far away from the elder stage to be covered, but that may not be as important for you.