Query posts using less than

How about something like this?

   $args = array(
    'date_query' => array(
        array(
            'before'    => array(
                'year'  => 2013,
                'month' => 2,
                'day'   => 28,
            ),
            'inclusive' => true,
        ),
    ),
    'posts_per_page' => -1,
);
$query = new WP_Query( $args );

Obviously you could set the exact date from a variable.

More info: https://codex.wordpress.org/Class_Reference/WP_Query