Should I buy the domain first or finish the site content first?

I have a new site deployed on Cloudflare right now, but it’s still using a test/preview URL.

The site works, but I’m still improving the content, copy, and page structure. I’m trying to decide whether I should buy and connect the real domain now, or keep working on the test URL until the content feels more polished.

From a launch/SEO perspective, is there any downside to waiting?

My current thinking is that using the real domain earlier might make things cleaner for URLs, Search Console, indexing, and redirects. But I also don’t want Google or users seeing a half-finished site too early.

How do you usually handle this when launching a new site?