If you are starting a remote gig, doing camera-on video 1 on 1s with all the people you I would encounter (and often one level above) was extremely helpful for me as it gave me a chance to introduce myself and set the context for those who were not involved in the interview process.
I would always finish by asking for advice on what it takes to be successful at X company, people loved that question and shared tips that shed light on internal culture rather than the typical platitudes. Good luck!