> My additional recommendation would be to try to identify limited-scope projects that contribute to your role and where you can start delivering some value.

If you are in a leadership role over a team then having a pre-chewed problem ready for new members of your team is a very useful thing you can do. I'm talking well defined problem with a clear path towards success. This helps the new member become use to the team and processes, and gives them an easy win to put some wind in their sails. Also, this can serve as a litmus test to their on the job performance.