When should I start the full-time return offer conversation?

Hi everyone! I graduated recently from college and also started an internship at a firm I really enjoy (I am on week 1). When I interviewed for the role about 2 months ago, the interviewer (which was the owner, it’s a small firm) mentioned that since I was graduating from school the goal of the internship for me was to prepare me for a full-time after the internship if there was good performance/good fit with the firm/I enjoyed the work. The role was mainly posted for current college students, but they took me with a little bit of a pay bump since I am a grad.

The internship has started good and besides doing the work, I am doing the “right” things such as building rapport at the office, asking insightful questions, connecting with people outside of my team, etc. This is also not my first internship so usually know how it can go. However, I am a bit worried because I am not the only intern anymore and two of them are rising college seniors, meaning it could get a bit more competitive. I do count with what the owner told me during the interview, but then again, it’s not guaranteed.

I want to make sure I am putting my best foot forward. I am wondering when would it be good to bring up the conversation again with the owner? (Mind you this is like my first week lol) How many weeks should I wait if I just got started? Or should I bring it up directly to my new manager? (Owner doesn’t directly supervise me). Any thoughts are appreciated, thank you!