Ravenous Bugblatter Beast of Traal
Yes, their propaganda education does imply that it's done deal. Then we hear that it's not -- in exactly what you quoted. So, if Mobius was telling the truth, it's still being worked on. So all we need that parts containing Loki(s) were "done" less than a Loki-lifespan ago.That's not quite how it was presented. The sacred timeline is indicated to be a fait accompli at this point, it's just that they don't yet know how it will end, because supposedly the Timekeepers are still working on that.
None of the TVA activities we've been shown are about pruning away already-existing independent timelines. They're all about nipping newly-branching timelines in the bud.
From the Thor movie we know Thor himself was around 1500 years old and Loki around 1070. That gives us plenty of time that "oh it's a single timeline" that we can still have plenty of pre-sacred-timeline Lokis about.