Do I have to invite my translators to every new project that I create?

I have the same translators working on all my Projects. Do I really need to invite them over everytime I create a new project?

Each project can be assigned to only one team, but you can have several projects assigned to one team. So you could create one big team with all needed collaborators and assign this team to multiple/all projects.
When you create a project, you have to select an existing team or to create a new team:

If you missed it and selected to create a new team, you can always go to the “Teams” Page, and add the new project to the existing team.