Do you think I should actually set up the business as fast as possible and try getting clients to test the need instead?
Short answer: No
Long answer: Sales is part of setting up the business...no sales=no business. I wouldn't do one thing for setup until I had an actual check in hand. No one likes to be cold called. Ask your family members, friends, friends of friends to see where they are struggling with IT. Go to a local business meetup and say you are in IT, ask for problems.