I’ve started a new job and there isn’t enough work yet. How do I avoid pretending to be busy?

My manager looked over and said, “All settling in?” I said yes. I’d spent most of that morning rereading the same welcome folder.

I joined a small events team nine days ago. The person I’m replacing is still here for another month, and the project I was hired to support has been delayed. I’ve completed the introductory tasks and asked twice what I should do next. Both times, the manager said she’d find something after her meeting.

I could keep asking, but I don’t want to become another interruption in a busy week. I could improve a few documents, but I don’t know which ones people actually use. Mostly I’m afraid that a quiet start will make me look unnecessary.

What would you do with the gap? How do I tell the manager I have capacity without sounding as though I expect every hour to be arranged for me?