I want to do the same but I live in a big city (millions of people). How do you recommend approaching this? There is no board/calendar that would get the attention of thousands of people and without that it's useless in a big city.
Additionally, an "MVP" could be a single HTML page, which lists all the recurring events, grouped by week-dat on a week calendar. For example, if there's a venue which hosts a weekly jam session on Thursdays, you could add that once and it would always show up for the "What's happening Thursday?" area. Usually there are a bunch of recurring events in any town, so the calendar page quickly becomes a useful "what to do today/tomorrow" guide, with minimal effort.
What makes you think that? Google/chatbots need a crawlable source. Instagram content is not a crawlable source. Be that crawlable source and they'll send the traffic your way. I get thousands of monthly visitors from Google alone. The next step in the funnel is to make them sign up for a weekly newsletter.
I'd also suggest a giant "purchase ticket here" button on every event page and measuring how many people click on it, it's infinitely easier to approach the organisers when you can easily whip out that statistic on your phone.
You could do something similar and then print out physical copies of it and hand over a few to local music venues, cafes, pubs etc to spread the word.