How can someone launch a prepaid debit or credit card program with a bank without being a resident of that country?

You do not need to be a resident of a country to launch a Pre-Paid Debit Card.

In many countries their are companies that provide such a service, but that would obviously be defeating the point (since you want to launch one directly).

You would need to have a registered business in that country, for the issuing bank to work with you. This would be the very basic requirement. If you can manage to get incorporated in the host country of issuance, the next step would be finding a bank to work with.