Restrict the users to post in the groups who haven't uploaded their profile picture

The only default fields when registering on a Discourse forum are:

Email*
Username*
Name
Password*

You can’t fill in data like avatar, bio, location, etc, during signup.

The only sign-up fields that can set as mandatory, besides the default ones except Name, are custom fields: Create and configure custom user fields

Alternatively, Custom Wizard Plugin 🧙 may help but I never used it, so I won’t know if it will address your request.