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.