It's funny since I used to have the opposite situation occur but now I do not see the first execution of the job.

// signature
public QuartzTriggerHandle doIndex( @Expiration Date when, @IntervalCron String cron )

// call
private static final String CRON_STRING = "0 0 0 * * ? *"; 
indexer.doIndex( new Date(), CRON_STRING );