How can one establish a profitable café without falling into any religiously forbidden acts?

There is no objection to opening a café if it adheres to Islamic regulations by prohibiting forbidden things like smoking and pornographic websites, and reprehensible acts like music and the mixing of men and women.

As for profitability, it should be referred to specialists. Among the means of attaining and blessing it are fearing Allah, relying on Him, supplication, seeking forgiveness, charity, honesty in selling, and not attaching one's heart to money.