What do you mean by "invite"? What would that look like?
My perspective of designers and product managers is that they like to own projects. FOSS generally works based on merit, where you first contribute and members of the project decide whether to accept it.
For developers this is easy:
- Contribute code
- Code is accepted or rejected
That's how it should work for design as well. Contribute some designs that you think will improve the UX and if they're desirable, someone will take up implementing them. If it's easy (e.g. a new logo), it'll get done right away, and if it's more involved, it'll get done as devs get time.
Project management is trickier because that requires buy-in from the devs. To get there, you need go earn their trust:
- help triage bugs (propose a severity system if there isn't one)
- help organize a roadmap
- do some leg work marketing whatever the project needs (go find designers if needed).
If you do a good job, they'll let you do the above more autonomously. But they're not just going to hand over decision-making to a rando off the street, especially since "they" can change day to day.
Developers don't like being told what to do (esp since it's usually a hobby), but they do want the project to be more successful. Designers and product managers are certainly welcome, but the onus is on any contributor to demonstrate the value they bring.