Cloudflare owns/leases fiber to form its own international network. A user's request hits a cloudflare server. if that server needs to contact the origin, it can exit from anywhere in cloudflare's network. If the origin is in the country which is wanting the block to happen they'd just ask the hosting provider to take the service down, otherwise CF would almost certainly be able to reach it from somewhere in their network.

You seem to be assuming that cloudflare's CDN is located in the country doing the blocking.

I'd imagine that CF's first act would be to remove any of the "offending" content from the country, at which point BGP blocking would no longer do anything.

Cloud flair is its own AS and they're definitely big enough to have global reachability with multiple paths.