Possible meanings are 1) "we persuade people of the truth of the gospel" or 2) "we persuade people that we are legitimate apostles." (See: [[rc://en/ta/man/jit/figs-explicit]])
This can be stated in active form. Alternate translation: "God clearly sees what kind of people we are" (See: [[rc://en/ta/man/jit/figs-activepassive]])
Paul wanted the the Corinthians to know what kind of people he and those with him were. "I expect that it is also clear to your conscience" or "I trust that it is also clear to your conscience"