I think this is a bit too passive of an approach to generating freelance work. Everyone that I know of in consulting or freelancing is actively approaching people, drumming up conversations and trying to find things that they can help with to get their foot in the door. Once you've delivered on some projects with those clients, then they'll typically start coming back and asking for more, but it's not realistic to think that you'll get people cold-calling you asking for your services simply because you talked to them on LinkedIn for 10 minutes.
Everyone I know in freelancing/consulting, including myself, does almost no work drumming up new customers.
Repeat business from long-term relationships, and word of mouth through referrals are my main source of new customers. I work through an agency that puts new projects in front of me, but most of my customers are long-term, and I got them through contacts.
Among your professional colleagues you have to cultivate a reputation as an honest person who can solve problems, someone who is easy and pleasant to work with. Then people will think of you and recommend you when they hear about an opportunity.
I'm on LinkedIn mainly to keep in touch with people I used to work with, but I have never used LinkedIn to get consulting/freelance work.
I know lots of people trying to freelance struggle with getting jobs. They're all over Upwork and Fiverr and the many other gig sites. That's piecework, it's not the same as consulting. I hire people from those marketplaces sometimes to do small short-term projects.
One goal for freelancers and consultants is to get to the point where you're the only person the customer talked to. You aren't interviewing or submitting proposals. I understand that doesn't sound realistic to someone just starting out, and I admit I had the advantage of decades of professional experience and a lot of contacts. I describe some of my experience on my web site, I don't think I'm particularly unique.
