Search engine optimization is important if you post events, even if you post them on social media. Without SEO, you're missing out on large numbers of people searching for an upcoming event. Even though they could search on social media, people's first instinct is to Google an event and choose the most relevant listing.
If you're talking about annual events, make sure there is a page listing the most current event. For previous events, create an archive page. You can link to events which already happened from the upcoming event page. You may not want to have Google crawl the archive page or it may return an event from 2018 when users where searching for the 2020 date of the annual event. This frustrates users and will prevent them from returning to your site.
You will need to organize your site by events. Keep the content on the page current. If the information from previous years isn't important, skip archive pages. You can add snippets from the last few annual events at the bottom of the page.
Learn event SEO. There is an Event Pack and Event Carousel in Google's search results similar to the local three pack. It appears at the top of the page so it has a higher click-through rate than the organic results below it.
Always use event schema to get a prominent listing. You need to include the location, event name, dates, images, the venue name, ticket information and price and performers, if applicable.
Link building is still important for event websites. It can make the different for your site's status as a featured snippet. Consider using important keywords in your event title even if they are not part of the official name. This can help you get more links back to your site from local sites. For more information click here https://www.reddit.com/r/SEO/comments/ezaxxy/cyclicaleventseocompetingwith_myself/.