I don’t think there is a one-size-fits-all approach when you want to contact someone new. I think it depends very much on the individual and what that person’s preferred communication channels.
I feel like I use LinkedIn begrudgingly these days. It is where business people tend to want to connect but groups and other fora seem to have become opportunities to spam everyone with some or other deal.
Now and then I know people who want to meet people. I enjoy connecting people (authentically) so I thought I’d offer to help.