SG-1's first experience with time travel came about accidentally when a massive solar flare, occurring at the same moment as gate travel during the intended mission to P2X-555, redirected the wormhole to within 70,000 miles of the sun, causing gravitational space/time warping. The resulting slingshot effect caused SG-1 to travel backward in time roughly 30 years, to August 4, 1969. For a moment the team existed in both time frames simultaneously, arriving at Cheyenne Mountain through the stargate before the gate seemed to vanish.
At the time, Cheyenne Mountain was a top secret missile silo, and SG-1 was apprehended as suspected Soviet spies. They were detained and interrogated by Major Robert Thornbird, who did not appreciate O'Neill's assertion that he was either Captain James T. Kirk of the Starship Enterprise, or Luke Skywalker. A young Lieutenant Hammond had also been stationed at the facility, and he recognized his own handwriting on a note Carter was carrying that said, "Help them. August 10th/ 9.15 AM, August 11th/ 6.03 PM." Before the mission began, General Hammond had recognized the cut on Carter's hand, and he had used Carter's research into solar activity and time travel to look up the time of two solar flares in August of 1969 that would allow the team to use a reverse slingshot effect to return home. Lieutenant Hammond fulfilled his destiny by heeding the note and helping SG-1 to escape.
The team hitched a ride with Michael and Jenny, a young couple on their way to Woodstock in their psychedelic bus, and they traveled across country on Route 66, arriving in New Jersey by August 10th. They sought out a young Catherine Langford in New York City and learned the location of the stargate in Washington, DC, also triggering Catherine's interest in renewing her stargate research. By entering the stargate a few seconds too soon, SG-1 was thrown far into the future, where they were met in a deserted gateroom by an adult Cassandra, who used a wrist device to activate the stargate and return them home. When young Cassandra was old enough to understand, Carter would tell her of her future role, thus completing the loop of time.
Cross Reference: Cassandra, George Hammond, Jenny, Catherine Langford, Michael, P2X-555, Stargate, Robert Thornbird, Time Travel
Episode Reference: 1969