Database

[{"_id":0},{"_id":1,"a":null},{"_id":2,"a":{}},{"_id":3,"a":{"0":"someValue"}},{"_id":4,"a":{"1625":"someValue"}},{"_id":5,"a":{"0":1,"1625":"someValue"}},{"_id":6,"a":{"7":"someValue","900":"someValue"}}]

Query

db.collection.find({$and:[{a:{$type:"object"}},{$expr:{$gt:[{$size:{$filter:{input:{$objectToArray:"$a"},cond:{$ne:["$$this.k","0"]}}}},0]}}]})

Result