SSL and first step of handshaking When I connect to a secure sever that has is equipped with SSL certificate.

Logically, the first step is the handshake to discuss the cipher suites etc.

However, the very first time my web browser does a DNS request and comes up with the location of the site, and my browser connects to the website even before starting the handshake, is this step secure (encrypted by the public key of the websites web server by getting its public key from the built in keys in the browser) or no?



Update: 
What I mean here, what happens the very first thing when I open the browser and type https://randomness.org the very first time my broswer (computer) and the server come in to contact. Is this connection secure?
If we assume that DNS (DNSSEC) and IP (BGP) are well behaved, deployed and used correctly then so far so good. You should be reaching the intended server.

If however there is an adversary between you and this server, then they may interfere with the TLS handshake, including but not limited to altering the chosen ciphersuites and public keys. Any alterations are detectable when we pass the certificate verification, key exchange and authentication steps. However if the client doesn't do all the correct verifications, they may be vulnerable to Moxie's sslstrip tool, which performs various attacks.