If there is a key it must be the willingness to be
    persistent, not give up the effort to enrich the
    network of connectedness. Here and there people do
    respond, and a relationship slowly begins to form.

I think that's 100% right. I've lived in NYC for almost 10 years and the sad reality is that people come/go frequently. I've found persistence to be the only consistent factor in building all the friendships over those years.

Yes you need to click with someone, but we determine that within 5 minutes of talking to a new person. A lot of people make the effort to build a new friendship, but get too discouraged from a lack of reciprocation. 5 no's in a row can definitely signal "not interested" (ha) but a lot of people are interested they just need more of a push.

It does come down to how badly you want to build that new friendship, but I think a lot of people are just not persistent enough at the beginning tbh.