You can also respond to job listings looking for contractors, and tell the recruiter that you've got a team that could work together. Sometimes that works.
I did agency consulting for 13 years, it is a constant hustle but can be a lot of fun.
Remember to always be looking for the next contract while working on the last one: make friends at the company, connect on LinkedIn. Don't be afraid to sell yourself, in fact nobody else is going to do it for you. You need an extravert on staff, or an introvert who can fake it (that can be even better).
Unsolicited advice: specialize at all costs. The more you can say things like (just an example here) "we are the experts at building typescript applications for SMB retail SaaS companies", the more likely you are to get hired, compared to the company who says "yeah we'll do anything for money". You want the person in charge to be able to look at your track record and say "these guys are a safe bet, because they've done this exact thing before."
If it may help, I'm based in the UK and mainly in the contractor market. I've got a very good team across the stack and we specialize in cross-platform mobile apps (mainly React-Native).
In my experience having a strong tech rep with actual development background goes a long way. I find most of my clients through Linkedin and handle the sales myself, then organize the work with my team that I've built over the years.
Happy to share more detail and get to know fellow hackers' experiences.
P.s. been lurking for a long time and this is my first comment! Amazing community