I'm in the onboarding phase. I was assigned a starter task and have been working on it. I haven’t done the work of asking questions on design choices (that part is pending).
I want to be ramped up after a week and am wondering how to spend the time. Should I go in-depth on overall architecture? Or spend time working on the codebase? Or is there something else I should do?
Zooming out, I recommend talking more with your manager and TL to figure out what the longer-term horizons are for you. From there, you can work backwards on what's best for you to do. For example, let's say the plan for your next 3 months is to deliver a big project in a specific part of the codebase. You can start preparing for that now by finding relevant stakeholders in that codebase, going through that code, etc.
Lastly, I recommend going through this onboarding checklist I shared with a new engineer that started at Google: "Started my 1st FTE SWE job and been on my team for just a few weeks - What should I do?". I think a lot of it can apply to your situation as well.
If you want to go super deep, check out our onboarding course: The Complete Onboarding Guide For Software Engineers
I want to be ramped up after a week
Where did you get this timeline from? One thing I'd do is be very explicit with your manager your ramp up timeline and how that will be measured.
Ideally, this is something you can add (or your manager can add) into the onboarding doc, as I talk about in this lesson: Create An Onboarding Doc
How you spend your time: code, meetings, 1:1s, design docs, etc will depend very much on your team, level, etc.