I don't think you could create a branching timeline just by doing something (like traveling to the past), but I think the alternate timelines may already exist and if time travel into the past is possible then it'll be by going to one of those alternate timelines.

As for the bootstrap paradox, I think it only becomes relevant in specific situations (like you travel to the past you in the same timeline and tell yourself how to make a time machine..), not in any possible situation in which you travel to the past. But, I don't think that traveling to the past on the same timeline is possible at all. I have a blog post explaining why. https://myriachromat.wpcomstaging.com/2020/06/30/on-time-travel/

There are some ifs, ands, and buts in that post--in other words some possible considerations (even if they're outlandish or unlikely, at least according to a certain point of view) under which time travel to the past in the same timeline may be possible, and in those cases maybe time travel involving the bootstrap paradox may be possible too:

(1) maybe the book you send past you on how you built the time machine arose in some organic way much like the chicken-egg paradox arose evolutionarily, but the domain under which it was created isn't limited to the timeline in question. Maybe there's a kind of meta-time in which the self-creating scenario in question (like the time machine book) could evolve in a progressively self-refining causal loop, or

(2) maybe the entire self-creating construct could have been sourced in the pure creativity of the universe--the same creativity that inspires things like great works of art, or maybe even biological forms (if you accept teleology). This would imply a worldview that's more like idealism ( https://myriachromat.wpcomstaging.com/2020/02/07/why-im-an-idealist/ ) than like 100% blind mechanistic cause and effect.