Honestly, I'd skip the whole "build your network first" trap. That takes ages and most people burn out before it pays off.
If you want clients now, go straight to the people who have the problem you fix. Pick one specific type of business, find 50 of them, and send a short message that shows you actually get their world. No credential dumps, no "15 years experience" bollocks. Just one observation about their business and one question. Something like: "Noticed you're hiring for X role, which usually means Y is becoming a bottleneck. How are you handling that right now?" That's it.
Out of 50, maybe 5-10 reply. Out of those, 2-3 turn into real conversations. And one of those might become your first client. Now you've got proof, a case study, and the confidence that makes landing the second client ten times easier.
The "no connections" thing feels like a wall, but it's not. Cold outreach bypasses the introduction game entirely. You don't need someone to vouch for you - you just need to say something relevant enough that a stranger wants to reply. That's how you start building the kind of connection that actually matters.
What kind of consulting are you moving into? and who's your ideal client?