This snippets is compatible even there is a year and month in the url.

Wordpress Pagination with "First" and "Last"

/**
 * Add first and last button to the
 * default pagination of wordpress
 *
 * Note: Don't forget to initialize your default 
 *       query to limit your post in pre_get_post hook
 *       
 * @var     string  $post_type  name of your post type
 * @var     int     $total_post number of total post to get the number of pagination
 * @return  void    pagination
 */
function first_last_pagination( $post_type, $total_post ) {
    global $wp_query;
    $archive_link = get_post_type_archive_link( $post_type );
    $current_link = ( isset( $_SERVER['HTTPS'] ) ? "https" : "http" ) . "://$_SERVER[HTTP_HOST]$_SERVER[REQUEST_URI]";

    /* Generate First Link */
    if( isset( $wp_query->query['year'] ) ) {
        /* Insert the year */
        $first_link = $archive_link . $wp_query->query['year'] . '/';

        /* Insert the month */
        if( isset( $wp_query->query['monthnum'] ) )
            $first_link .= $wp_query->query['monthnum'] . '/';
    }
    else {
        $first_link = $archive_link;
    }

    /* Generate Last Link */
    if( isset( $wp_query->query['year'] ) ) {
        /* Insert the year with the current page number */
        $last_link = $archive_link . $wp_query->query['year'] . '/page/' . ceil( $wp_query->found_posts / $total_post ) . '/';

        /* Insert the month with the current page number */
        if( isset( $wp_query->query['monthnum'] ) )
            $last_link = $archive_link . $wp_query->query['year'] . '/' . $wp_query->query['monthnum'] . '/page/' . ceil( $wp_query->found_posts / $total_post ) . '/';
    }
    else {
        $last_link = $archive_link . 'page/' . ceil( $wp_query->found_posts / $total_post ) . '/';
    }

    /* Check if the current link is the first page to hide the button */
    if( $current_link != $first_link )
        echo '<a href="'. $first_link .'" class="first">First</a>';

    echo paginate_links( array(
        'base'      => str_replace( 999999999, '%#%', esc_url( get_pagenum_link( 999999999 ) ) ),
        'format'    => '?paged=%#%',
        'current'   => ( get_query_var('paged') ) ? get_query_var('paged') : 1,
        'prev_text' => 'Previous',
        'next_text' => 'Next',
    ) );

    /* Check if the current link is the last page to hide the button */
    if( $current_link != $last_link && ceil( $wp_query->found_posts / $total_post ) > 1 )
        echo '<a href="'. $last_link .'" class="last">Last</a>';
}