Mongo aggregation based on Dates between on more Collections - mongodb

Question

I'm using Mongo Aggregation with Spring Data to retrieve data from 4 collections.
My problem is that I want to add a filter based on the createdAt on 3 of these collections.
Here the examples:
Animal
{"_id":123,"name":"Lucky","age":3,createdAt:"2022-02-01 10:00:00.000Z"}
{"_id":456,"name":"Joe","age":5,createdAt:"2022-02-10 20:03:00.000Z"}
Cat
{"idAnimal":123,"toy":6,createdAt:"2022-03-01 10:00:40.000Z"}
{"idAnimal":456,"toy":2,createdAt:"2022-02-10 20:05:00.000Z"}
Pet
{"idAnimal":123,"meal":3,"medicine":false,createdAt:"2022-03-01 10:00:40.000Z"}
{"idAnimal":456,"meal":4,"medicine":true,createdAt:"2022-02-10 20:05:00.000Z"}
What I mean to do is to get all the Animals with a Pet collection created gte(2022-03-01). The expected result would be the first cat, Lucky.
In my code I tried this
final List<Criteria> criteria = new ArrayList<>();
criteria.add(new Criteria().orOperator(
Criteria.where("createdAt").gte("2022-03-01").lte("2022-03-02"),
Criteria.where("Cat.createdAt").gte("2022-03-01").lte("2022-03-02"),
Criteria.where("Pet.createdAt").gte("2022-03-01").lte("2022-03-02")
));
and my Aggregation set up is:
Aggregation aggregation = Aggregation.newAggregation(
Aggregation.lookup("cat", "_id", "idAnimal", "Cat"),
Aggregation.lookup("pet", "_id", "idAnimal", "Pet"),
Aggregation.unwind("$_id"),
Aggregation.match(new Criteria().andOperator(criteria.toArray(new Criteria[0]))
)
);
I tried to swap the criteria, querying the Pet first, but didn't go as expected. When I run this, I get no result.
Do you have any tips? Is it possibile to execute an aggregation on Dates over multiple collections?
Thank you in advance!