See the script in this thread for an idea: query-minimum-date-using-rest-service. Note the comment on line 35. You would use the EditDate field.
Have you checked this page: Sync workflow examples? The topic Workflow Example 4: Setting up sync using LayerQueries contains this:
"layerQueries": {
"1": {
"queryOption": "useFilter",
"useGeometry": false,
"where": "region = 'Southwest'"
}
},
The "where" would be edited to something like:
"where" : "EditDate >= DATE '2016-05-29 18:30:00'"