[{"car":{"model":"Astra","productions":[{"modelOne":{"dateOfCreation":"2019-09-30T10:15:25.026+00:00","dateOfEstimation":"2017-09-30T10:15:25.026+00:00","someOnterInfo":"whatever"}},{"modelTwo":{"dateOfCreation":"2017-09-30T10:15:25.026+00:00","dateOfEstimation":"2019-09-30T10:15:25.026+00:00","someOnterInfo":"whatever"}}]}}]

db.collection.aggregate([{$addFields:{dates:{$map:{input:"$car.productions",in:{$let:{vars:{model:{$arrayElemAt:[{$objectToArray:"$$this"},0]}},in:"$$model.v"}}}}}},{$project:{_id:1,"car.model":1,"car.earliestDateOfEstimation":{$min:"$dates.dateOfEstimation"},"car.earliestDateOfCreation":{$min:"$dates.dateOfCreation"},}}])