Hansen's time was good enough for 13th fastest qualifier and a meeting with Cuban Lisandra Guerra Rodriguez.
Hansen lost narrowly, saying she needed "about five more metres of track" to overtake her rival.
"I stuck to my race plan and executed it as good as I could on the day," she said.
"This women's sprint team has only been together for six months... so I guess we're building experience. Lisandra competed at the last Olympics so she's got a lot more experience in the bank than I do."
Hansen is a full-time air traffic controller with airways, so would appreciate more than most the complexities of an arrival at Heathrow in July.
Whether she gets there looks likely to be in the hands of the New Zealand Olympic Committee after BikeNZ indicated they would nominate her.
"I'm 99 per cent certain she's fulfilled the UCI requirements," coach Stu MacDonald said. "We've got to put the nomination forward to the NZOC and it's up to them whether they select her to compete in the sprint."
MacDonald is hardly an impartial observer, but he believes the experience would be invaluable looking ahead to the Glasgow Commonwealth Games and the Rio de Janeiro Olympics.
"She hasn't got the experience the other top female riders have so... the experience she'd get from London would help her so much."
MacDonald said Hansen's times were world-class, but she had some work to do on the tactical side of head-to-head racing.
The early sprint session was dominated by Anna Meares. The 2004 Olympic gold medallist clocked 10.782s around the Hisense Arena, shaving .011s off Lithuanian Simona Krupeckaite's time.
The best-of three quarter-finals take place tonight, while the semifinals and medal rides are held tomorrow.
