Lack of work

I started a new job that is fully remote about 3 weeks ago. I haven’t recieved a whole lot of training. It’s mostly been Job shadowing or “this is how you do it” type stuff. They don’t really have a training schedule. It’s all hands on. I’ve been doing a lot of basic administrative tasks. I got my official assignment this week and I have done maybe 2-3 hours of actual work and that may even be too much. My team lead keeps reaching out asking if I’m all good or need more work. I usually say yes because I’m just sitting around waiting for assignments. Should I be doing more? Should I be asking my manager for more work or that I’m not getting enough? They don’t want to overwhelm me but if anything I’m underwhelmed.