I'd say this is a pretty specific English expression, right? There are some Swedish idiomatic expressions that fit in that context, I'd choose either Vi sätter vår lit till Gud or Vi litar till Gud. The translation they give in Wikipedia is I Gud vår förtröstan which sounds archaic to me. None of those 3 are expressions I'd recommend to learners to use in other contexts though.
Could you be more precisely? To me there is a big difference in believe and trust. Still trust was accepted as an answer. Is that a mistake or are you disunited about this?