As @brianOrtiz said in his comment, the answer to this is found in the licenced stargate novel Moebius Squared. In the prime universe, George Hammond (knowing that he survived into his 50's and was therefore effectively immortal) put himself at extreme risk in saving Sam's father's Jacob. Her father, and Hammond's example of conspicuous bravery led her to join the USAF.
In the alternate universe, her father died in Vietnam, she barely knew George Hammond and her mother discouraged her from joining the service.
“You remind me of my dad,” Carter said, without thinking.
“Really?” Sam looked faintly embarrassed. “I never knew mine. He was
killed in Vietnam when I was a baby. My mom raised me.”
“My mom died when I was in my teens,” Carter said slowly. “Dad took
care of us as best he could. That’s part of why I went into the Air
“Mom would have had a heart attack if I’d even suggested it,” Sam
said. “I had the hardest time talking her into letting me get a car,
never mind flying a plane. I can’t imagine…” She shook her head. “She
was determined to keep me safe. She wasn’t going to lose me like she
“Did you ever know George Hammond?” Carter asked, and Sam nodded.
“He was my father’s wingman, the one who brought back his body. Danyel
said that in your time he commanded the SGC?”
“I remember when I was little he used to send me Christmas presents,”
Sam said. “But Mom didn’t like having him around — too many bad
memories, I think. She lost touch. That — I’m sorry about that, from
what Danyel’s said. He must have been an amazing man.”
And that was more of what the Stargate had done, Carter thought. The time loop that had thrown the team back to 1969, when they’d given
Lieutenant Hammond a note from his future self in order to get back to
their own time — she’d wondered how that had changed him, and if it
had, indirectly, changed her father. And now she knew. In her time,
Hammond had saved Jacob Carter’s life that day in Vietnam, and maybe
he had taken a crazy risk because he knew that somehow he was going to