Is Badgey part of a bootstrap paradox?

I was rewatching LD 4x07 “A Few Badgeys More” when Badgey’s ramble about seeing past, present, and future as he ascended gave me a question: if Badgey has become a non-linear, omnipotent being, what is the impact on the timeline? My thought is that delta insignia seen in Starfleet and past human organizations may actually be part of a bootstrap paradox; the delta insignia inspires Badgey, and then eventually, Badgey, after becoming non-linear and being part of all time and space, causes the the delta insignia that inspired his form in the first place.