Personalizing the hero image, how do I keep LCP fast?

my hero image changes per audience, and the hero image is my LCP element on every landing page. i am worried that choosing it at request time means it swaps in after load and my LCP regresses.

what i want is the correct image already present in the first paint, not a default that gets replaced once the personalization resolves. is that achievable, and how do i optimise it so the LCP element is stable?