Billion dollars buys a lot of clerks
It is of order a thousand dollars per recipient.
You could process all the payments by hand for that. Perhaps with a very simple fund transfer system and a few spreadsheets.
It is interesting that the Tax office consumes roughly 1% of GDP, which is exactly what it consumed back in the 1950s before any computerization.
The bigger the project, the less likely it is to succeed. A billion dollar project has no chance at all.