Magenta, The above are all good answers. When the subject is relationships "to swoop" can mean... ....to steal someone away from an existing relationship.... Examples: The young girl at the table in front of us is trying to swoop in on her best friend's man. Her boyfriend is out of town. Now is your chance to swoop in on her. Television host Conan O'Brien is ending his contract with NBC, and FOX Network is ready to swoop in on Conan in order to create its own late-night talk show.

Hello Magenta, It is a metaphor as fdmaxey mentioned, comparing the act of a hawk. pouncing suddenly. It indicates a sudden ,quick action of seizing the opportunity to befriend this girl.

"Swoop in" implies great speed. The relationship was established in an unusually short time for a friendship that strong. The image is of a hawk or eagle that swoops (dives) in fast to get something.