Exclude old events from WP_Query with date saved in a `meta_key`

You need something like the following:

$args = array(
    'post_type'         => 'events',
    'posts_per_page'    => 1,
    'meta_query'        => array(
        'meta_key'          => 'event_start_date',
        'type'              => 'DATETIME',  // You can also try changing it to TIME or DATE if it doesn't work
        'meta_value'        => date( "Y-m-d" ),
        'meta_compare'      => '>',
    ),
    'order'             => 'ASC'
);