Grammatically, there are other places where the genitive refers to Christ as the object.
In Philippians 3:8, Jesus Christ is described as the object of knowledge. In 1 Thessalonians, he is described as the object of hope. In both these cases, it is clear from the context that Paul is not talking about Christ's knowledge or Christ's hope. There is no grammatical reason why the same can't be true of pistis christou.https://www.thegospelcoalition.org/blogs/trevin-wax/faith-in-christ-or-faithfulness-of-christ/