How do you connect a website to Cloudflare without downtime?

Create the Cloudflare zone and review every imported DNS record before changing nameservers. Compare it with the active zone at the current provider, including A, AAAA, CNAME, MX, TXT, CAA, and service-specific subdomains. Automatic scanning can miss records that are rarely used.
Add the site to Cloudflare while the old nameservers remain active. Configure the correct origin address, choose an SSL mode that validates a working origin certificate, and decide which web records should be proxied. Mail and many verification records should remain DNS-only unless their provider explicitly supports proxying.
Test the origin directly or use a controlled local hosts-file entry before delegation. Confirm that the server accepts the domain, HTTPS works, and Cloudflare IP ranges are not blocked. Preserve the current DNS zone and note the old nameservers so the change can be reversed if needed.
Change nameservers at the registrar, then monitor DNS responses, web errors, forms, payments, and mail. Keep the original hosting configuration active during the delegation transition. Once traffic is stable, document the Cloudflare account, security settings, cache rules, and emergency method for temporarily disabling the proxy.