Demonstrating to Google that your brand is respected and in demand by your peers and your audience, is essential to pass the EAT test.
You can generate a buzz about your brand in your peer community and with your audience. You can reinforce this curated buzz by including links from your site to the third party content that mentions your brand. Then, Google is sure to understand that all of the media attention is, indeed, about you, and thereby improve your E-A-T credentials.
A better E-A-T score will be a significant help to your overall SEO strategy and branding factors like a knowledge panel.