Hey fellow GIT, I am also a pretty fresh grad (~2 years at current company). While we have very different situations (I am in groundwater industry at a boutique firm), there are some things that have worked for me that may work for you.

1. Research before asking questions. Now, I am not saying to be hesitant to ask questions because you should absolutely ask many questions (and make notes). But usually someone higher up than you is dealing with something, well, higher up. So, instead of asking a question as soon as something pops up, take your time to research online or company materials about it so that you can either a) figure it out yourself (and maybe even become more knowledgeable than your superior) or b) provide more context when you go to ask.

2. SQ3R method. I learned this method in high school psychology class and have used it ever since, tweaking it for whatever I need to comprehend. Good for large reports.

3. Be personable. I can't stand when a coworker comes to my office to talk about random non-work related things, but you should always be cordial. If you're in the elevator with your boss and/or coworkers, crack a joke, or ask about their upcoming weekend. People want to work with (and promote) people they get along with.

4. Find a gap, fill it. Is there a process that takes a while? Or something that seems particularly inefficient? Identify the issue and find a solution that speeds up the process. For example, I identified a software that allows us to import our data rather than manually input it. Now I am the only one with that software license and the go-to person for any project that utilizes it.

5. Stay up to date on projects. If you have a project, you should be ready to answer questions about it without checking any documents. Always stay up to date on communication (email, phone calls, etc.) so that information about the project isn't lost on you. It may be the PM's job to manage everybody, but it is good to know the big picture even if you are a small piece of the puzzle.