Currently, it is practically impossible to use the Serverless Inference API for that purpose. It used to be a daily quota, but now it is a monthly quota, and even Pro subscribers only get a monthly quota of $2.
Beyond that, you are charged on a pay-as-you-go basis. You will not be charged unless you add a payment method…
If you expect a large number of requests, it would probably be slightly cheaper to use the Inference Endpoint (dedicated).