と知り合って

after meeting; since getting to know

→ と
phrase Uncommon #8,929
after meeting; since getting to know 知り合う means “to meet” or “to get to know someone.” The particle と marks the person you meet, and 知り合って is the te-form. In questions about how long two people have known each other, the phrase is often followed by どのくらいになりますか.
JA: ジャックと知り合ってどのくらいになりますか。
EN: How long have you known Jack?

あなたはジュディさんと知り合ってどれぐらいになりますか。

How long have you known Judy?

ジャックと知り合ってどのくらいになりますか。

How long have you known Jack?

ルチアニと知り合ってどれくらいだ?

How long have you known Luciani?

— 預言者 (2009)

でも数年前に母はある男と知り合って…彼の言うままにこのモーテルを建てたんだ

But a few years ago, my mother met a man... and built this motel just as he told her to.

— サイコ (1960)