。
She came to trust him before long.
Literal
[topic-は] before-long him [object-を] trust [come-to-ようになる-past].
~ようになる ('come to do, become able to do') is the standard pattern for marking a change in habit, behavior, or ability — often gradual rather than sudden. 信じる ('trust, believe') paired with ~ようになる gives 'came to trust' — a process of gradual acceptance. Compare 信じた ('trusted [punctually]') for a sudden moment of belief. まもなく here colors the change as relatively quick despite the gradual frame — 'before long.' Note 信じる vs 信頼する: 信じる ('believe, trust') is the everyday word, while 信頼する ('have confidence in') is more formal and weighted.