How do you win clients in a trust-based, referral-only industry like manufacturing? (I will not promote)

I’m starting an agency, that builds websites with RFQ capture, sets up Google listings, and runs LinkedIn for small manufacturers in India. I’m confident it helps, since most units I’ve looked at have a basic site and get nearly all their business through contacts, so new buyers have nothing to go on when they search. The problem is getting owners to take it seriously. Most don’t see a website as a business problem, many are wary of agencies, and cold messages get ignored. For people who’ve sold to traditional or non-digital businesses: How did you get your first few clients when you had no case studies? What made owners trust you enough to take a call? Is a heavily discounted pilot a good way to get proof, or does it just attract the wrong clients? I’m happy to share what I learn. Any advice appreciated.