Hey Dan! 👋
Great question on the timeline. Right now custom domain publishing isn't on the immediate roadmap for the Generate API, so I don't have a specific date I can share.
That said, if this is something you'd find valuable, I'd love for you to drop it on our feature request board! We use Canny to track requests, and it really does help the team prioritize what to build next: https://ideas.gamma.app/
Even a quick post with your use case would be super helpful. If other folks upvote it, that gives the product team a clear signal. Plus you'll get notified if/when it moves forward!
Let me know if you have any other questions about what the API can do in the meantime. Happy to help you find workarounds if there's a specific workflow you're trying to build