How to update inserted_at timestamps?

I have a list of records that are to be sorted by the inserted_at column, and I would like to test the sorting functionality. In Ecto, I would create a list of the records and use Repo.update to update the inserted_at column with a calculated value so that the records have different timestamps.

I was able to work this out when I made the inserted_at attributed writable and passed it as an attribute to the update action

I would like to have the inserted_at field as a private attribute so that users cannot update it via the form, but this approach does not return updated values.

In my resource I have:

attribute :inserted_at, :utc_datetime_usec do
  writable? true
  default &DateTime.utc_now/0
  match_other_defaults? true
  allow_nil? false
end

...
update :update do
  argument :inserted_at, :utc_datetime_usec

  accept [:email, :language, :creator_id, :tenant_id, :inserted_at]

  primary? true
end

And In the test I have:

for invitation <- invitations, i <- 1..length(invitations) do
  invitation
  |> Ash.Changeset.for_update(
      :update,
      %{},
        private_arguments: %{inserted_at: time_before_or_after(-i * 12000)},
      authorize?: false
    )
    |> Ash.update!()
end