Help with 365/Dynamic Dist. Group - Auto add and Calendar

Hello,

I would like to create a group that automatically adds new members to it and has a group calendar associates with it. It seemed like a dynamic distribution group was the way forward to add members automatically, but it is also adding all of the regular distribution groups to it (not a big issue, but here are some other emails I'd like to filter) and has no calendar. A Microsoft 365 group has the calendar association, but I cannot find a way to automatically add a member when it is created. Is there an easy way to achieve this?

Thanks!