Does the following work:
<?php
$args = array(
'post_type' => 'event',
'posts_per_page' => -1,
'post_status' => 'publish',
'meta_query' => array(
'relation' => 'AND',
'date_clause' => array(
'key' => 'event_start_date',
'value' => $today,
'type' => 'DATE',
'compare' => '>='
),
),
'orderby' => array(
'date_clause' => 'ASC',
),
);
Code untested