[cross] {one's} mind

to come into one's thoughts or mind momentarily

The idea of traveling the world has crossed my mind many times.
During the meeting, a solution to the problem suddenly crossed his mind.
It never crossed my mind that I would meet my old friend at the event.
As she walked through the park, a strange thought crossed her mind.
It didn't even cross his mind that he could win the competition until someone mentioned it.