The startdate of the calendar is not set by the plugin itselves, but by the jquery based fullcalendar. You can set any options of the fullcalendar by append it to the shortcode.
To make the calendar start on 2013-04-01 you should do something like that:
{events_calendar; weekMode="variable"; year=2014; month=3; date=1}
Notice that the month start by 0 (=january)