[{datesArray:[{/** should include*/start_date:ISODate("2021-01-01"),end_date:ISODate("2021-02-01")},{/** should include*/start_date:ISODate("2021-02-01"),end_date:ISODate("2021-03-01")}]},{datesArray:[{/** should include*/start_date:ISODate("2021-01-01"),end_date:ISODate("2021-02-01")},{/** should exclude*/start_date:ISODate("2021-11-01"),end_date:ISODate("2022-01-01")}]}]

db.collection.aggregate([{"$addFields":{"inputDate1":ISODate("2021-01-01"),"inputDate2":ISODate("2021-12-31")}},{"$match":{$expr:{"$allElementsTrue":[{"$map":{"input":"$datesArray","as":"d","in":{$and:[{$gte:["$$d.start_date","$inputDate1"]},{$lte:["$$d.end_date","$inputDate2"]}]}}}]}}}])