The UU Churches are often very focused on their socialization side, with an old joke being that the UU sacrament is the social "miracle" of turning water into coffee.
There are a lot of more secular/atheist attendees of UU churches and UUs tend to embrace the diversity and the spectrum of beliefs. It's not a bad idea to give your local UU church a try if you haven't already.
[1] The interesting history of it is that both the Unitarians and the Universalists (once different groups) split from the mainstream Christian churches surprisingly early and relatively much more quietly compared to the Protestant revolution. The Unitarian dispute, especially, dates back the Nicene Convention that resulted in the Nicene Creed still central to modern Roman Catholicism and still often referred to by Protestants as well, although the organized church is quite a bit newer than that originating dispute in which the Trinitarians won the orthodoxy; UUs will tell you've they've been bucking orthodoxy for centuries.
To me it's not a "attract them" problem, it's a "keep them" problem.
I know that I've long considered myself a UU "irregular", which makes me "part of the problem". I show up as I feel like it when the whim hits me or there's a lecture/speaker I want to hear that week or I generally just feel a need for some coffee with a group I know I can typically count on to socialize with. Without the implicit coercion of "traditional" services have behind them telling people they must show up every week, UU can be seen as having a bit of a disadvantage on that front in keeping/maintaining/growing their communities over time. (The little UU church that is my favorite in my hometown is not quite 150 itself yet, I don't think, but probably shares a lot of similar tales of growth and shrinking over a nearly as long of a lifespan.)
At that point, so far as my advice may be, for what little it might be worth, finding repeat visitors that become irregulars that become regulars are a marketing problem like just about any other social club or an MMO videogame. There probably are things to draw from some of how those cope (or don't) with very similar problems. Help people feel welcome, help them feel engaged, help them find reasons to keep coming back.
That's a nice phrase, and it seems to describe be at the moment as well.
In Silicon Valley I've seen non-theistic churches sprouting up. I believe the Society for Ethical Culture on New York is similar.
For one thing, full membership requires you to tithe a fixed percentage (2%) of your income to the organization. Maybe I'm just being cheap, but I don't make a ton of money in research and that coupled with living in the most expensive area of the US makes me less inclined to seek out membership in their congregation.
I also feel weird about how they discuss their founder, Felix Adler. The number of times they invoke him seems almost like it's a cult of personality for him / he serves as a Jesus stand-in, and while I can't say I feverishly dislike the man, that was a huge turn off. If the group's observances were less centered around him and more concentrated on a broader variety of humanist figures, I would be able to get behind them a bit more.
The last issue I have with Ethical Culture is that it felt very monocultural / like an echo chamber. I'm fairly liberal by most standards, but I like to have exposure to individuals with different viewpoints from my own, be they conservative or libertarian. In Ethical Culture, any group other than die-hard liberals would meet with stiff opposition rather quickly and this was something I wasn't very comfortable with when I did attend services there. When I was religious, my church congregation was a much better mix of political perspectives (and even theological disagreements occurred occasionally).
In NYC, I've had much better experiences with the Secular Humanist Society of NY. It's much less formal, much more cost-effective for an expensive city (their meetings are in the back rooms of bars for the most part and yearly membership is only around $20 last time I checked) and it feels a lot more egalitarian / less hierarchical.
Or does that deeper topic interplay with meeting and socializing with people?
It seems as people in general become less religious, there's less of a default gathering place. But I've noticed that various types of fandoms seem to be filling in some of that gap. For example, if you have an interest in old computers and games there's a couple dozen big shows all over the U.S. every year and it's my understanding that many people have formed regular friendships because of these shows.
I almost wish there was a "Church of the Rational Mind" that met for service every Sunday morning at a local University auditorium, and you could hear lectures on various topics for an hour, then socialize afterwards. The Bible provides fodder for a tremendous number of sermons, on many topics, but there isn't the same kind of focused equivalent book for secularists.