Idea validation stage - cold reachouts

Wondering how you guys think about it -
I'm working on validating an idea, and trying to talk to as many potential clients to understand if what I identified is a real pain.
While I'm versed in the industry, I don't have many connections directly with my target audience, so I'm resorting to cold reachouts through LinkedIn.

The reply rates I'm getting so far are AWFUL. About 2 replies for 40 reachouts, 1 of which wasn't relevant at all.
Anyone here had experience with the same type of cold reachout? any magic formula for making those cold reachouts work?