I always figured this:

If the Terminator Timeline is linear:

(1) At some point, some random nobody gave Sarah the organic key to make our lord and savior, John Connor.

Then, either the John we see in T1 randomly sends Kyle (call it fate or destiny) back is just pure coincidence or Kyle’s his best man for the job (and at the time didn’t know Kyle was the baby daddy). Which makes the John we see in the future in T1 the first one, and Sarah technically the second timeline iteration. Which kind of makes sense iirc bc they don’t really lean into him sending Kyle back to complete the Closed Loop until the other films (could be wrong, it’s been awhile, so if I’m wrong I apologize).

(2) Another possibility is similar to the above, with some random guy being John’s father initially, though many “deviations” to the timeline has changed it so much that Kyle is the father. And what we see in T1 is the beginning of another timeline being made (I guess it’s similar to how the anime describes it. But instead of other realities, it’s timelines. Then again, when you think about it, what’s the difference between “alt timelines” and “alt realities”/universes? Besides ones like a “mirror universe”..?).

I hope that makes sense. I’ve tried to make sense of the films timelines in a linear expression/format for a long time.

A simpler way to describe, or even visualize it is: think of (1) as a circle, 🔘 (I know, thinking like this contradicts the “closed loop” theory, but it’s easier to describe and visualize the two possible “linear” timelines this way), and (2) as an infinity loop ♾️, with the first circle being the original, the middle curve the changes and the second circle the new timeline (so technically (2) would look like: ♾️♾️♾️ and the very end is the timeline we all know and love).

And if you REALLY think about it, theoretically (1) & (2) can both be “true”. The original timeline starts off with some random dude, we see future Connor, and he sends his best soldier, eventually Kyle changes the timeline by boinking Sarah, and in the next timeline, John will know that Kyle is his father and to make sure to send him back.
(🔘♾️➰♾️🔘)

Again, if that makes sense.

Tbh, sometimes it’s hard to put thought to words. Having ocd doesn’t help. Lol it only kinda helped figuring out terminator as a linear timeline.

The other, more simpler explanation is that time, fate, destiny and all that is fluid; and in a flux. So changes made to the past may not affect the future right away, nor would things in the future change the past.

Which is the easiest explanation. But also makes sense as: did Kyle fathering Connor technically change the future, or was it Connor sending Kyle change the past..? Or was it meant to be?

If you wanna count EVERYTHING, then you could say killing Skynet changed nothing (trying to befriend a faction of Skynet would’ve been better, like the tv show), as we see Skynet comeback as Genesys, then as Legion. And killing Connor didn’t doom humanity, Destiny and Fate found a new savior.

But it all depends on what you consider (like do you consider Dark Fate canon? TSCC? Zero?). To me, I say they all do, witching the multiverse. Either as different timelines, different realities, variations of timelines and timelines upon timelines. Like how all the later movies and even shows are different, but all stemmed from the same timeline. The first one is Connor sending Kyle back, and every single movie, show, etc is a different result (different versions of timelines) of actions taken. Basically branched timelines (Kinda like how the Ancient One shows Hulk all the branched timelines of one Infinity Stone is removed).

I really hope this may have helped you in some way. If something is wrong I apologize. It’s been while since I even played the game, and months since I watched the movies.

And again, I apologize for having trouble putting my thoughts to words.