Database

db={"product":[{"_id":"5fb55eae3fb1bf783a4fa978","title":"Test Product 1"},{"_id":"6bb55e883fb1bf783a4fa96a","item":"Test Product 2"}],"shipment":[{"_id":"afb68eae3fb1bf783a4gb542","title":"Test Shipment 1","shipDate":"2019-01-01","contents":[{"product":{"$ref":"product","$id":ObjectId("5fb55eae3fb1bf783a4fa978")},"quantity":10}]},{"_id":"8pb55eae3fb1bf783a4fa769","title":"Test Shipment 2","shipDate":"2020-01-01","contents":[{"product":{"$ref":"product","$id":ObjectId("5fb55eae3fb1bf783a4fa978")},"quantity":10}]},{"_id":"8pr55eae3fb1bf783a4rt587","title":"Test Shipment 3","shipDate":"2020-02-01","contents":[{"product":{"$ref":"product","$id":ObjectId("6bb55e883fb1bf783a4fa96a")},"quantity":10}]},{"_id":"8jk89eae3fb1bf783a4jo324","title":"Test Shipment 4","shipDate":"2020-02-01","contents":[{"product":{"$ref":"product","$id":ObjectId("5fb55eae3fb1bf783a4fa978")},"quantity":10}]}]}

Query

db.shipment.aggregate([{$match:{"shipDate":{$gte:ISODate("2020-01-01")},"packages.contents.product.$id":"5fb55eae3fb1bf783a4fa978"}},{$unwind:"$packages"},{$unwind:"$packages.contents"},{$unwind:"$packages.contents.product"},{$match:{"packages.contents.product.$id":"5fb55eae3fb1bf783a4fa978"}},{$group:{"_id":null,"total":{"$sum":"$packages.contents.quantity"}}}])

Result