I’m not sure I understood, but this may help: you can turn off the initial infowindow (the bubble). It’s usually off by default unless you have initialopeninfo=”true” in the shortcode.
If you want to leave the infowindow on, you can still sort the POIs by date. Turn off the MapPress alphabetical sorting with sort=”false”. Then WP should sort by post date (by default), or you can use one of the other sorts here: