The problem to solve is that these clubs exist already with low membership. Join a local Masonic lodge, or other local social org if you want to meet men you will learn from.
Boy Scouts, DeMolay and other boys youth orgs got their start in the 1910’s, joined by young men without fathers who were lonely due to their life situations. Many just need someone to take their hand and show them how to break the ice.
I joined the Lions about three years ago. Our local chapter was defunct, so I got it going again.
Now we have about 40 members (for a town of 500, that's pretty damn good).
We get together to do volunteer and fund raising events. But mostly we meet twice a month to eat supper and bullshit/play cards/pool/darts.
It's awesome.
I think we're going to bring back the formal dances they used to have in the 40's-60's. I think that would be fun.
Masons and the Scottish Rite (and even the Boy Scouts and DeMolay to some extent) have religious components that exclude people like me.