Aggregate recursive tree structure (parent reference) - node.js

Question

We are trying to build a simple CMS that can manage pages and its subPages. And every subPage can also have subPages etc.
The Problem we are currently facing is that we receive a flat tree after the second level and we would have to reorganise the tree with JS.
Is it possible to receive a real tree structure (see "desired output") without the use of JS.
The following tree structure is currently used:
[{
_id: 1,
name: "top-level",
parent: null
},{
_id: 2,
name: "second-level-a",
parent: 1 // top-level
},{
_id: 3,
name: "second-level-b",
parent: 1 // top-level
},{
_id: 4,
name: "third-level",
parent: 2 // second-level-a
}]
We are currently trying to receive the complete tree via this query:
Page.aggregate([
{
"$graphLookup": {
"from": "Page",
"startWith": "$_id",
"connectFromField": "_id",
"connectToField": "parent",
"as": "subPages",
"maxDepth": 1,
"depthField": "depth"
}
}, {
"$match": {
"options.parent": null
}
}
]).exec((err, pages) => {
if (err) {
res.send(err);
return;
}
res.json(pages);
});
What we are receiving is something like this:
[
{
_id: 1,
name: "first-level",
parent: null,
subPages: [
{
_id: 2,
name: "second-level-a",
depth: 0,
[...]
},{
_id: 3,
name: "second-level-b",
depth: 0,
[...]
},{
_id: 4,
name: "third-level",
depth: 1,
[...]
}
]
}
]
With this output it's not directly visible where third-level is placed inside the tree. The desired output should look like this:
[
{
_id: 1,
name: "first-level",
parent: null,
subPages: [
{
_id: 2,
name: "second-level-a",
depth: 0,
[...]
subPages: [
{
_id: 4,
name: "third-level",
depth: 1,
[...]
}
]
},{
_id: 3,
name: "second-level-b",
depth: 0,
[...]
}
]
}
]
The question is, is this even possible to achieve using MongoDB in combination with mongoose or do we need to sort the result with JS.