I've been a software developer for 20+ years, and almost all of my work has been on things I can't show to potential employers. Tell a story about how you made an impact, use screenshots or video to supplement, but don't try to "prove" anything. If they don't believe you, then you don't want to work there or you need to get better at telling your story.
(This doesn't apply to designers, or people trying to get a job based on UIs they've created.)
(This doesn't apply to designers, or people trying to get a job based on UIs they've created.)