You can manipulate the main WP_Query just before it asks the database for posts. Looking for an existing _thumbnail_id meta field should suffice, so using the pre_get_posts filter, something like this might work for you:
add_action("pre_get_posts", function($query) { if(!is_front_page() || !$query->is_main_query()) { return; } if(!array_key_exists("meta_query", $query->query_vars)) { $query->query_vars["meta_query"] = array(); } array_push($query->query_vars["meta_query"], array('key' => '_thumbnail_id','compare' => 'EXISTS' ) );});The conditional return at the start of the function is there to only target the main query on the front page, but leave alone any other queries (so it doesn't hide your posts without thumbnails from the archives, for example).