Most of the latency of a TLS handshake (which equals the minimum latency for the first response on a HTTPS connection) comes from round trips. You need 1 for TCP connection establishment. And 1 to 2 (depending on the TLS version) for the TLS handshake.
300ms would be rather on the high side. RTTs with todays infrastructure are often 30-50ms if you hit an Edge server (opposed to a server around the world). So you should end up up at around 100ms for the complete TLS connection establishment.
300ms would be rather on the high side. RTTs with todays infrastructure are often 30-50ms if you hit an Edge server (opposed to a server around the world). So you should end up up at around 100ms for the complete TLS connection establishment.