The premise of the original film The Terminator, is not that changes are happening as time travel occurs. In that film, a straightforward causal loop plays out.
- Skynet is created by Cyberdyne, and it wipes out most of humanity.
- A human resistance is formed, John Connor becomes a successful leader in it.
- In a hail mary move, Skynet sends the Terminator back in time to prevent John Connor from being born.
- The resistance takes over the time travel facility shortly thereafter, John sends his father, Kyle Reese, back in time.
- John is conceived.
- The Terminator is destroyed in a Cyberdyne facility, Skynet is created based on the advanced technology salvaged from the Terminator's remains. See step 1.
The film plays out half of this, with the other half being flashbacks and exposition from John. In this film, it's a clear causal loop, there's no mention of 'no fate but what we make', there's no mention of any other terminators traveling through time. When it came time for a sequel, those elements were added to this universe.
So in the original timeline, Cyberdyne created Skynet, based on advances in tech they developed from salvaging the remains of the Terminator that was left in their facility at the end of the film. In addition, Kyle was always John's father.