Recruiters are one way, not necessarily the best in the long run but a good short-term stopgap approach if you need to quickly find clients.

In my opinion the preferable long-term sustainable path is pretty much like in most businesses: Become useful and become noticeable. Create solutions and talk about it. A company website, blog, conference talks, networking events testimonials for instance are useful components of a marketing plan for a consultant.

As for the second question I'm not sure this is the right attitude. For example analysing a company's software creation process and pointing out ways to improve it is serious engineering but it doesn't involve writing a single line of code and often is more about human communication than hard engineering facts.

Value creation starts when you first talk to a prospective client not just when you write the first line of code.

Most large companies have vendors. You can typically become a vendor via their supply chain management system. They usually have a web page where you can register your company, provide a list of services, and such. You also need to qualify by submitting liability insurance documents and such.

This is the best way to route around recruiters. It is hard work though. They usually have vendor fairs where you have a booth and give out brochures, advertise, network with internal managers...