。
As soon as she spotted me, she started running toward me.
Literal
She [topic-は] me [object-を] spots [when-と] immediately my direction [toward-へ] began-running.
見つける specifically means 'to discover by looking, to catch sight of' — the moment of recognition rather than mere perception. The unmarked 見る covers 'see / look at,' but 見つける captures the discovery instant. Japanese routinely splits perception verbs into 'general perception' and 'directed/successful perception' triplets: 聞く ('hear/listen') vs 聞こえる ('be audible'), 見る ('look/see') vs 見える ('be visible') vs 見つける ('find by looking'). The combination of 見つける with ~とすぐに here makes the recognition feel immediate and triggering.