Is there a common expression for "origin of everything"? What could it be?

Genesis is the term generally used:

• the coming into being of something; the origin.

• a beginning or origin of anything

• This chapter will trace the genesis and development of the oldest human civilisation.

also dawn:

• A first appearance; a beginning:
  • the dawn of history.

'Ur', as in the phrase 'Ur example' or 'The Guttenberg Bible is the ur-book'.

[Edit 03/04/2015]

"Forming words with the sense of ‘proto-, primitive, original’."

Source; Wictionary http://en.wiktionary.org/wiki/ur-

"The Ur Example is the oldest known example of any given trope. Ur-' is just a German prefix meaning 'proto-, primitive, or original.'"

Source; TV Tropes http://tvtropes.org/pmwiki/pmwiki.php/Main/UrExample

An "ur-book" would be (one of) the oldest known example(s). In that context, the Guttenberg Bible would not be an 'ur-book' but it would be the ur-example of the printed book.

The ENIGMA machine could be thought of as the ur-computer. It almost certainly wasn't the first functional computer but it is the first example that is generally known. Charles Babbage's analytical engine could also be thought of in this way, as it was conceived at an earlier time, but it was entirely theoretical and no contemporary examples were ever constructed.

Are you looking for the term, "Big Bang?" Genesis in Greek means origin, creation, generation or formation of everything γένεσις, or 'gignesthai.'

A "requisite step" or ignition semantically different from genesis.

My answer would be ab ovo gemini or ab ovo for the beginning of beginnings. What you're looking for is most probably fundamental, elementary or basic. Depending on your relation to given person you might want to top it with a "my dear Watson."