The original script for The Terminator makes it abundantly clear that Skynet developed and built the "Time displacement" technology on its own, using the Terminators as its workforce:
REESE: ...it had no choice. The defensive grid was smashed. We'd taken
the mainframes... We'd won. Taking out Connor then would make no
difference. Skynet had to wipe out his entire existence. We captured
the lab complex. Found the...whatever it was called...the
time-displacement equipment. The Terminator had already gone through.
They sent two of us to intercept, then zeroed the whole place. Sumner
didn't make it.
This is then backed up by the official novelisation for Terminator 2: Judgement Day, in which we (the omniscient reader) learn of the reasoning behind Skynet's research into time technology, for use as a weapon:
Until one day the tide of battle turned, and Skynet, in a desperate
burst of brilliance, devised time displacement, the first tactical
time weapon. It sent a lethal emissary back through time to find and
eliminate Sarah, so that John Connor might never be born.
It may also interest you to know that according to the official novelisation for Terminator: Rise of the Machines, the fundamental theoretical basis for the TDE was done by Einstein and Hawking in the 50s and 1980s (prior to Skynet becoming active):
The super black project, funded by the Department of Defense, Central
Intelligence Agency, National Reconnaissance Office, and National
Security Agency, was designed to create an artificial wormhole.
Einstein had first suggested such a phenomenon, and the English
theoretical physicist Stephen Hawking had done some work on the
possibility. But the problem was power. By most calculations the
wattage needed to create an infinitesimally tiny wormhole, in other
words a passageway through space-time, would take almost all the
energy ever produced in the universe since the moment of the big bang.
Clearly Skynet used its gigantic brain to overcome this limitation.