When you setup a new data integration and set the data to Sync All Leads, the process will begin as soon as my +plus leads finds a new listing. If you wish to post older leads from your system, you will need to create a historical search and push the data to over to your 3rd party platform. 

Learn how to create a historical search - https://portalhelp.myplusleads.com/support/solutions/articles/6000042684-searching-historical-fsbo-and-expired-leads

You can only sync 1000 listings at a time. If your search contains more than 1000 listings, try breaking it up by month or price range.