You have not really described what the ACTION does. But the Parent record can know via a Summary field of the Maximum [Date Created] of the child records.
The Excel upload process is manual anyways, so my suggestion is to run an ACTION on the Parent records subject to a filter that the children have been uploaded (re Maximum date above is say today or this month - whatever your billing cycle is).
So, how to act on those parents. One way is to have a dedicated table called like Trigger Billing with exactly 1 record in it. It will be Record ID# = 1. Set up a formula field on the Parent records equal to a 1, which are all now children to that single Trigger Billing record.
Then you will do the upload manually and then when you are ready to trigger billing, you will toggle a checkbox on the Trigger Billing and that will kick off the ACTION. You can make a URL formula button to flip the value of that checkbox.