The unusual (English) word order has the effect of emphasizing the part which is moved to the front from the normal order. The basic meaning is unchanged: the trusting is being done by "we" in both forms.
The normal order, "We trust in God", places more emphasis on the first word, the subject, "We" (although the emphasis is not large, simply because this is the normal order for most sentences).
Putting "in God" first emphasizes that, and it has a stronger emphasis because the order is not the ordinary order.
