read only date field after save

You can use a form rule to detect if the record has been saved.

But for some reason, form rules do not allow the use of the [Record ID#] field.

You can make a formula numeric field call Record ID# mirror with a formula of

[Record ID#]

And use it in a form rule

When multiple conditions
The user is in the Role. (Role)
The Record ID# mirror is > 0

Make read only [Date field]

And make the field required on the form.