There is no free use of the API. The model usage is charged per https://openai.com/api/pricing/
It is easy to misunderstand the state of your API account, because OpenAI previously offered free trial grant credits that were automatically added to your account, and which expired after three months. If you made an OpenAI account for using ChatGPT, you might not have even known the API existed and that you had some credits, now expired.
So you are correct. To make use of the API for programmatic model access, you’ll need to be able to pay for the usage by purchasing an account credit first. Here’s where you can add a payment method and purchase that credit, starting at $5.
https://platform.openai.com/settings/organization/billing/overview
The program to give free trial credits has been discontinued.