Honestly, and this isn’t something I’d ever thought of until just now, it’s probably reasonable to assume that most Starlink ground terminals (the ones that users install at their homes and businesses) sit in a fixed location. It would be complex to do, but I suspect you could probably get quite good orbital positioning in reverse by using all of the fixed ground terminals as a giant reference set. If the terminals themselves have GPS receivers built-in, the whole system could pretty readily bootstrap itself (each GT sits and continuously averages its own GPS position and clock offset, then transmits that up to the overhead SVs as they pass by). Even without GNSS receivers in the GTs, though, you could probably still rely on the Starlink-owned GTs to know their own positions very accurately and augment the whole thing using the “static user GT” assumption. GTs that did move would just be treated as noise in the whole thing.

It’s been a while since I’ve done this kind of math, but it sounds like a really fun problem!