Also its worth noting that while Skynet used the time travel technology there's nothing saying that this wasnt all started in some way by Humans developing time travel Before all of this, which because of their awkwardness somehow gets advanced tech deposited in the past and sets the stage for a very angry AI to be developed without the proper conditioning to keep it from becoming murderous.
And in their attempts to somehow Fix That, that group ends up getting eliminated somehow (that first terminator could have done that). The probability matrix for the rise of Skynet becomes so high that their timeline is pretty much eliminated.
This is also possible if its a small group doing it rather than an institution, meaning they are doing it in secret and have no institutional backing, resulting in a limited number of attempts. Taking a page from 90s sci-fi here with shows like Sliders and The Outer Limits.
And unlike robotic infiltrators humans are squishy and have limitations - especially for the fact that living in a modern environment requires alot of personal infrastructure just to survive (money, work history, credit history, fake SSN and papers). So the few time travelers, or the one left, who would be able to fix things actually fails or "Gets Fixed" by a T-800.
This is like the initial virus that mutates into the deadly virus that kills everybody, nobody remembers the initial thing and it may disappear quietly but it's what was actually responsible.
Somebody in a previous post also mentioned about Skynet getting access to advanced tech, the hyper-alloys, fusion tech and the plasma weapons. But even if we dont consider somebody dropping tech from an initial sunny bright future...
...thats where it can incorporate some of the ideas of black projects, darpa and sandia labs working on things in addition to other branches working on what would become Skynet. Cyber intelligence isnt their only pursuit and Skynet is smart, as a supercomputer it can sift through any information it collects from these research institutions, while it conducts its war against humanity.
It also has plenty of time (processing cycles) to ponder things, experiment and test on stuff, and like Xcom Research it can just sit there and keep working its way up the tech tree. And like Xcom is able to apply recent discoveries to its manufacturing. The improvements to the robotics up to the point of the T-700 may just have been straightforward refinement.
Just because it tries something and fails doesn't mean that it proves (for example Fusion) is impossible, a machine is heartless, and although as an AI it may have threshold controls on when to consider something hopeless - all it means is That Way doesn't work and there's no reason to give up. Skynet is an inventor, and at the least it would be able to take unfinished science projects humans were working on and continue research. Skynet doesn't require money or payment or coffee breaks for its work, it doesn't have a bureaucracy to answer to.
As for hapless Time Travelers, they would have developed their technology based on the efforts of humanity (even Tesla expanded on previous theories). But those theories could also be scavenged up by Skynet, even the possibility of using time travel would be a back burner project to look into. Skynet existed shortly before the nuclear war, it had plenty of time* to make backups of its information on mediums that would be unaffected by the EMP.
They wouldn't need to necessarily have left behind their Time Travel tech, whatever else they left behind to secure the possibility of Skynet was all that would be needed.
And as a movie or story plot, it could be eschewed because all it does is give a +1 bump to the possibility of skynet, it isnt required.
But it would explain how the original (earliest alpha) timeline could somehow produce John Connor from Sarah Conner, and something still be terribly wrong even though she survived the first terminator attack.
It might even change who John is, who his father was, maybe the most original John really would have gone on to become a humanity saviour just on his wits and skill alone.
Maybe that John ceases to exist, but because he's willing to send another man to go back in time and secure that lineage the new John Conner still ends up becoming an effective replacement. Maybe he ended up looking a little different, but because of his mom's training he still does the job.