Need to get documents from the 1st of the month in Mongo & Redash

Question

I need to get documents from a collection for aggregation starting from the 1st of the current month.

I'm trying this with $dateFromPart, but that isn't working as expected, since it's returning 0 documents, while manually specifying the date new ISODate('2021-10-01') returns the expected result.

I assume it's because I can't use $dateFromParts in the $match stage.

db.messages.aggregate([
    {
        "$match": {
            "timestamp" : { 
                "$gte" : { 
                    "$dateFromParts" : {
                        "year" : { "$year" : new ISODate() },
                        "month" : { "$month" : new ISODate() },
                    }
                }
            }
        }
    }
])

Extra info:

• I Have to use the aggregate, I will be doing some more $group operations later.
• I can't use javascript to build dates before the query. This query will be used in Redash, which only accepts a json input, and you can't run any javascript there.
• Obviously I can't use new ISODate() in redash, I would have to use their built-in $humanTime, but the point remains the same.
• The messages collection is big. Over 10 Mil documents, with an index on timestamp. So I need to avoid COLSCAN like the plague.
• Using Mongo 3.6 (I know, time for an upgrade)
• Bonus points if I can do the query from the 1st of the month, three months ago.