The site is not fully down
A 503 is an HTTP response. Something — origin, load balancer, or maintenance page — accepted the connection and answered. That is different from a timeout or a DNS failure, where no application response arrives.
Operators use 503 for overload, deployments, and planned maintenance. Retry-After, when present, is a hint to wait. Refreshing immediately in a loop usually makes overload worse.
What you should do
Wait and retry once or twice. If you run the site, check capacity, health checks, and whether a dependency (database, cache, another API) is down. Visitors should not clear caches as a first step — the server already said it is unavailable.