I have no complete answer, but I'd like to share what happened in my neighborhood.
TLDR we neet to meet them where they are
A group of climate-biodiversity activists tried to get people to come to educational workshops.
They got a few of us, the ones that were already interested in the topic and who are priviledged enough to spend time and energy on other stuff that work, commuting, family care and basic survival/comfort. But after that, the workshops were empty.
So they tried a different approach. For over a year, they organized activities perceived as fun and/or useful by the neighborhood.
Think collective soup cooking and soup parties for which didnt have to pay, kids activites for parents who have trouble paying for child extrascholar stuff, furniture/cosmetics DIY cheap and well made, bike repair afternoons, drinks at one's or the other's place...
Beginnings were not easy, but little by little word got out, they got better at understanding what other people actually need, trust began to emerge, disagreements found a space to be discussed and overcome....
Not everything went well, some people take and never give back, some other are outright jerks (mostly out of racism and misogyny), some (like me) don't like group settings and almost never come, half the original organizers burnt out...
But the result is impressive. Last time a workshop about climate change was organized, they had to schedule 6 sessions over a month to fit everyone. That's still a very tiny part of the inhabitants but it's so much more than at the beginning!
The last vegetarian "cook and eat" gathered a lot of people, we see a lot more bikes in use in the streets, more plants at the windows and people talk to each other much more often...
And I believe the neighborhood is nearing the point where popular education can happen, be it about environment, politics, societal evolution etc.
Were this to happen in multiple neighborhoods across a city, in multiple cities across a country and in rural areas structures (which I don't know a lot about), well maybe you could start getting people interested about socialism, maybe I could get them interested in anarchy ;)
So while I don't think this is going to be enough in and of itself but it looks like a first step that's necessary to go further.
I also believe this is gonna take a long time, face strong backlash and many setbacks, and I don't believe it's gonna happen before I die. But being a part of enabling socialism or anarchy to happen at a later date is a legacy I'd be more than happy with.