So just FYI, Apple is really weird and inconsistent about this.
I did the exact same thing: bought an M1 Max 14" MBP, figured my CC gave me accidental damage so I wouldn't need AC+, but decided I wanted it anyway about a month-ish before the one year warranty would be up.
TLDR I did not end up being able to get AppleCare. If you really want it, go to an Apple Store ASAP and plead your case.
There was a brief period of time where Apple and the Apple adjacent press made a big deal out of Apple allowing you to purchase AppleCare up through the end of your one year warranty as long as you can prove the device is in working condition but i'm pretty sure they're phasing this out and trying to pretend like it was never a thing.
Here's how my experience went:
1. Looking at Apple's website in multiple regions, mention of this has been mostly scrubbed from the Apple Support pages, although you can still find references if you look hard enough.
2. Apple Support by phone is completely useless. They won't run any diagnostics or even let you make an appointment to have it physically examined to assess eligibility. Each rep will tell you something different ("That was never a thing," "I don't see that anywhere," "That was/is only for some regions but I can't tell you which ones," "This doesn't apply to your product." "I'm sorry your misinformed, and if it was on the website it was a mistake/not for your region." )
3. You need to have purchased in and be be in a region that was eligible for the program to begin with. I bought in the US but was in Japan. I was visiting the US soon so set up an appointment but ended up not being able to go to the appointment due to life getting in the way.
4. You can try either walking into an Apple Store and waiting or opening a support ticket for something else to make a reservation, but you can't just make a reservation for AppleCare+ examination. Although as I said, I didn't end up going for this, I've been there enough recently to know, expect to waste a good chunk of your day, be ready to politely argue your case/escalate.
Overall a really ****** experience that convinced me Apple really just didn't want my money (and reminded me that my accidental insurance coverage is good enough I can just "accidentally" drop it in the bath if I ever have a problem and get reimbursed.)
My advice if you really want to do this is: Be prepared. Print out proof that this was Apple's stated policy when you bought your Mac (news articles, screenshots or prints of Apple Support Pages, etc.) Don't waste your time on the phone, go into a physical Apple Store on a day you have a lot of free time. You need to have bought your Mac in an eligible region (I believe the US was one,) and be in/able to visit an eligible reason to start this process. Be patient. Please report back if you are successful!