What does it look like to be a faithful presence? It is seeking to serve those in your sphere of influence by creating a beneficial culture for them, thus creating a faithful witness for Christ to which others will be drawn.
Just as the Jewish exiles in Babylon were exhorted to live and do good in the foreign and pagan culture, so are Christians advised to do good in whatever circumstances or culture they find themselves.
While the popular belief for changing the world by changing hearts, minds, etc. is a thoughtful one, it is not necessarily biblical. Rather, Christians should focus on doing good if they want to change the world.