How can a website become automatically copyrighted?

One would assume that the owner of the site has some records of the creation of the site. Copyright protection runs for so many years now, I have a hard time imagining a website element that would continue to be used until the copyright term ended.

An original website is protected by copyright law as soon as it is "fixed in a tangible medium of expression." A computer or server hard drive would qualify as a tangible medium of expression and the website would be "fixed" when it is saved on the hard drive. Thus, you are correct that a website is generally protected by copyright law when it is created. To address your question about challenges with verifying creation dates, it is important to remember that enforcing rights under copyright law requires proving, with evidence, that you have valid rights and that someone infringed your rights. You would need to prove that your website was created on a given date before it was copied to prove that someone copied your website. In addition, you would need to prove that some copied your website as opposed to independently creating his own website that happened to look similar.

It works as you expect - you create original content on your webpage - and you own the copyright for that content. For proof of ownership, and to register the copyright - you could save screen shots in hard copy form - pdf for example.

The automatic copyright rights apply even if you cannot verify the creation date. You would like to be able to verify the creation date. Website and software creation dates are not virtually impossible to confirm. All you need is a witness and/or forensic data found on computers.