"When a new branch timeline is created, did the universe of that branch timeline already exist as an identical duplicate of the main universe until it's divergence?"

I think that's the case, yes.

So do you think the Sacred Timeline was comprised of infinite universes with some universes having minor to semi-major differences in detail, such as Sylvie's and Classic Loki's, and other universes being identical duplicates of the main universe with zero differences?

(Sorry if it's worded weirdly)

For what I understood, the Sacred Timeline was the collection of all the universes where there was no possibility for other variants of He-Who-Remains to exist, such as Kang.

So even a completely different universe, with completely different events, was allowed to exist by the TVA as long as there was no risk to Kang or other to come into being.

So, yeah, minor details difference, major details difference or identical universe, all where comprised in the Sacred Timeline where there was just He-Who-Remains.

^A universe CANNOT be created after the Big Bang.

In a universe you can travel time, nothing is impossible.

It does. That alternate universe didnt start at the moment of this decision. It just went on a different ways since that point, and until that point it just went on the same path, but was not "The" main universe.

So I guess what The Watcher said may have just been a metaphor as Peggy Carter deciding to not go to the booth was when the alternate timeline had been created, but the universe was always there.

It's called quantum physics. Look up Shrödinger's Cat.

For the Timestream/Sacred Timeline/Rope, we already know that each strand of the rope is a universe and its timeline but I think that there are infinite identical copies of the original universe born from the first Big Bang and they all share the same one strand because they're all the same universes with the exact same timeline.

However, when one of these identical universes' timelines start to deviate from the original universe's path, a new branching strand develops containing that divergent universe and its new diverging timeline. You could see The Watcher's line as, "The moment that created a new divergent universe."

Earth-199999 is the original universe as well as the main one from our perspective while Captain Carter's universe is an identical copy that shared the same strand until its timeline diverged and created a branching strand. Just my theory based on what I've seen but it makes the most sense.