For anyone encountering this issue, I was able to get it to work using the following params:

$params = array(
            'filtering' => array(
                array(
                    'field' => 'created_time',
                    'operator' => 'GREATER_THAN',
                    'value' => strtotime($start_date)
                ),
            ),
            'limit' => 1000
        );

The Reason seems to be that time_range is only supported by the Insights API and not the Marketing API