mongodb - group by on ~ 1.3 million records - mongodb

Question

{"messageId": "123124", "writtenAt":"2017-04-26T15:16:36.200Z", "updatedAt":"2999-12-31T23:59:59.999Z"}
{"messageId": "123124", "writtenAt":"2017-04-26T15:21:30.230Z", "updatedAt":"2999-12-31T23:59:59.999Z"}
The structure of the collection is above. Aside from the mongo id, it has an id called 'messageId', in a collection we can have multiple entries with same 'messageId' but has different 'writtenAt' field value. Have a compound index: messageId (desc), writtenAt (desc).
Now, wanting to do a group by on messageId so I would only get the the latest one (max writtenAt value). I have the following query but it's taking very long I haven't even gotten a result yet (more than 10 mins then I stop, collection has over 1.3 million records):
db.messages.aggregate(
[{ "$match": { "updatedAt": { "$gte": { "$date": "2021-02-26T06:59:51.738Z" } } } },
{ "$sort": { "messageId": -1, "writtenAt": -1 } },
{ "$group": { "_id": "$messageId", "doc": { "$first": "$$ROOT" } } },
{ "$replaceRoot" : { "newRoot" : "$doc"}}
], {allowDiskUse: true});
If I add an explain with executionStats, I can see it's picking up the index:
[
{
"$cursor" : {
"query" : {
"updatedAt" : {
"$gte" : ISODate("2021-02-26T06:59:51.738+0000")
}
},
"sort" : {
"messageId" : -1.0,
"writtenAt" : -1.0
},
"queryPlanner" : {
"plannerVersion" : 1.0,
"namespace" : "db.messages",
"indexFilterSet" : false,
"parsedQuery" : {
"updatedAt" : {
"$gte" : ISODate("2021-02-26T06:59:51.738+0000")
}
},
"queryHash" : "3141BBC5",
"planCacheKey" : "6858F892",
"winningPlan" : {
"stage" : "FETCH",
"filter" : {
"updatedAt" : {
"$gte" : ISODate("2021-02-26T06:59:51.738+0000")
}
},
"inputStage" : {
"stage" : "IXSCAN",
"keyPattern" : {
"messageId" : -1.0,
"writtenAt" : -1.0
},
"indexName" : "idx_messageId",
"isMultiKey" : false,
"multiKeyPaths" : {
"messageId" : [
],
"writtenAt" : [
]
},
"isUnique" : false,
"isSparse" : false,
"isPartial" : false,
"indexVersion" : 2.0,
"direction" : "forward",
"indexBounds" : {
"messageId" : [
"[MaxKey, MinKey]"
],
"writtenAt" : [
"[MaxKey, MinKey]"
]
}
}
},
"rejectedPlans" : [
]
}
}
},
{
"$group" : {
"_id" : "$messageId",
"doc" : {
"$first" : "$$ROOT"
}
}
},
{
"$replaceRoot" : {
"newRoot" : "$doc"
}
}
]
Any idea how can I can improve? After retrieving the latest messages by messageId then planning to do some pagination slicing after.
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