Database
[{"_id":"id1","properties":[{"type":"value1","start_date":ISODate("2022-03-03T00:00:00.000Z"),"end_date":ISODate("2022-05-03T00:00:00.000Z")},{"type":"value2","start_date":ISODate("2022-05-15T00:00:00.000Z"),"end_date":ISODate("2022-06-08T00:00:00.000Z")},{"type":"value3","start_date":ISODate("2022-06-21T00:00:00.000Z"),"end_date":ISODate("2022-07-04T00:00:00.000Z")}]},{"_id":"id2","properties":[{"type":"value2","start_date":ISODate("2022-03-03T00:00:00.000Z"),"end_date":ISODate("2022-05-03T00:00:00.000Z")},{"type":"value5","start_date":ISODate("2022-05-15T00:00:00.000Z"),"end_date":ISODate("2022-06-08T00:00:00.000Z")},{"type":"value1","start_date":ISODate("2022-06-21T00:00:00.000Z"),"end_date":ISODate("2022-07-04T00:00:00.000Z")}]}]
Query
db.collection.find({properties:{$elemMatch:{type:"value2",start_date:{$lt:ISODate("2022-06-01")},end_date:{$gt:ISODate("2022-06-01")}}}})