Convince is a hard word… a whole industry has been trying to crack that nut for 25 years now.
Google chooses what it wants to show, and the algorithms can be quite neurotic about it. You and I can look at the same SERP result at the same time and see a different presentation just based on location, device, or a flip of the coin.
Honestly, you might be better investing your time in something else that will deliver results.
But, if you are determined to try, there are three directions you’ll need to research depending on what you want.
Rich results with featured images
Polish up your open graph data, and create structured data like Article, BlogPosting schemas… product courses, etc. Depends on what you’re presenting. If you have good clear data for Google, AND your site is considered authoritative on that keyword, it’s more likely to show your image as visually relevant to the search topic.
Rich snippets & featured snippets
This is in-between, also fed by open graph and rich results data.
Knowledge panel
The far right-side panel that shows for certain keywords, usually sourced from Wikipedia, Wikidata, Google My Business, etc. It’s “authoritative” information about the entity you’ve searched for.