It really depends on the company culture. At my startup, yes. At my previous startup, no. In some places unlimited PTO is meant to be a perk for responsible employees; don't be constrained to X days and be flexible as long as you're getting stuff done. In others it's just an accounting dodge so the company doesn't have to carry the PTO balances as a liability on their books and pay them out when an employee leaves. Of course it's challenging to determine the difference because in the latter case, managers are reluctant to state the truth out loud as they prefer to be perceived as the former case.
Ask a peer you trust, or your manager if you trust them to give you guidance on the norms around PTO in your group and not the company line. “Hey, should I put more time in before taking a couple days off?” You’ll get “no, that’s fine,” “yes, probably,” or “weeeeeeeellll, it’s up to you" (which means yes).
Also observe how much PTO people are really taking. You’ve been there 7 weeks, have any team members taken vacation? If “unlimited” means even “2-3 weeks worth” then math would indicate some folks should have.
Per your comments you’ve gotten guidance on how much PTO is normative but not the nuances around it, like how early you could take some or what kind of notice/approval you need. Again, feel free and ask your manager but when the policy is deliberately two-faced they usually can’t give you a straight answer so a peer might be better.
Then you know the norms and can follow or push them at your discretion.