Check if the current user is author of first comment

Helper function

Here’s a helper function (untested) to check if a given user ID is the first commenter for a given post ID:

/**
 * Check if a given user ID is the first commenter for a given post ID
 *
 * @param int   $user_id User ID
 * @param int   $post_id Post ID
 * @return bool True/False
 */
function wpse_is_user_first_commenter( $user_id = 0, $post_id = 0 )
{
    $first_comment = get_comments( 
        [ 
            'status'  => 'approve', 
            'number'  => 1, 
            'order'   => 'ASC', 
            'orderby' => 'comment_date_gmt',
            'post_id' => (int) $post_id, 
        ] 
    );

    if( empty( $first_comment ) )
        return false;

    return $first_comment[0]->user_id === $user_id;
}

Usage example:

Check if the current user is the first commenter of the current post:

if ( wpse_is_user_first_commenter( get_current_user_id(), get_the_ID() ) )
{
    // ...
}

Hope you can adjust it to your needs!