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 TC

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.