How to make"invoicing payment" optional for customers?

Summary

It is not possible to create an invoice for a subscription that has an "immediate charge without payment". However, you can use workarounds to achieve this.

Using Chargebee's Hosted Pages

The plan for which the subscription is created should have a trial period or a full discount to avoid immediate charges and checkout without payment; it applies only when you use Chargebee's hosted pages.

Using API or Chargebee's admin console

Set the auto-collection status of the customer as OFF while creating the subscription and later use the Update payment method link to get the card details.