"One of the first steps I would take is to listen intently, observe, and take great notes every time I am invited to a meeting or find myself in the middle of a team conversation. I find that project managers juggle a ton of details and action items. Making sure I am up to speed on the details is an easy way to contribute.
From there, I would seek to schedule one-on-one time with them to review project plans, learn about their customers, and learn about their individual project management style. I would want to support each of them in a way that works best for them, so I would ask them what they need and how I can best be of service.
I would proactively take on anything I could easily do without direction and check in regularly for new assignments and for feedback on my performance. I feel those three strategies would help me to develop strong relationships with any project managers I have the opportunity to work with if hired for the assistant project manager role."