[{"id":"1234567890","date":"YYYY-MM-DD","contents":{"0":{"content":{"id":"1111111111","name":"Name 1"}},"1":{"content":{"id":"2222222222","name":"Name 2"}},"2":{"content":{"id":"3333333333","name":"Name 3"}}}}]

db.collection.aggregate([{"$addFields":{"newField":{"$objectToArray":"$contents"}}},{"$addFields":{"newField":{"$filter":{"input":"$newField","as":"z","cond":{$eq:["$$z.v.content.id","1111111111"]}}}}},{"$addFields":{"newField":{$size:"$newField"}}},{$match:{newField:{$gt:0}}},{$project:{contents:1,date:1,id:1,}}])