How can I find the first post in a category that has a featured image and then return the get_the_post_thumbnail()?

The ID of the featured image is stored under the meta key _thumbnail_id, so we can do a query for a single post that has this key:

$args = array(
    'posts_per_page' => 1,
    'meta_key' => '_thumbnail_id',
    'cat' => $cat_id
);
$latest_thumb = new WP_Query( $args );

if( $latest_thumb->have_posts() )
    return get_the_post_thumbnail( $latest_thumb->post->ID );