How can I display a specific user’s first published post?

The following query retrieves the oldest post of a specified user/author:

$user_id = 42; // or whatever it is
$args = array(
    'posts_per_page' => 1,
    'post_status' => 'publish',
    'author' => $user_id,
    'orderby' => 'date',
    'order' => 'ASC',
);
$first_post = new WP_Query($args);
if ($first_post->have_posts()) {
    $first_post->the_post();

    // Now you can use `the_title();` etc.

    wp_reset_postdata();
}

If you want to show the first post a specific user wrote (no matter what the post’s publish date is set/altered to), then you have to use 'orderby' => 'ID',.