A calendar link in the first message reads like a pitch. What works better for coaches and consultants is offering two specific times in their timezone, once they have shown interest.
One coach we work with got 6 calls in week 1 and 7 calls in the first 2 weeks, with about a 30% close rate, using a short video and plain replies instead of links.
The first message is only there to get a reply. The booking comes after that.
What do you send when someone says "sounds interesting"?