Long story short
[1]satoshi came up with the idea of bitcoin somewhere from mid of 2007 and they were working on the code right then.
[2] As UserU said, bitcoin.org was registered on 18 August 2008. Then on 22 August 2008 satoshi sent Wei Dai a mail about their Electronic Cash project along with a whitepaper. This was the first written document mentioning about
bitcoinE-cash. Note that bitcoin wasn't named back then. You can find the first whitepaper draft here :
https://draftable.com/compare/rCuIgdwzImUI[3] On 31 October 2008 Bitcoin whitepaper was published with minor changes in the ecash document. The name E-cash was renamed to Bitcoin. The registering of bitcoin.org and publishing of E-cash paper to Wei Dai were only written documents of the not-still materialized project.
[4] On 16 November 2008 satoshi sent the basic codebase to Hal Finney, Cryddit and other several cypherpunks to have a code review on Bitcoin.
[5] On 3 January 2009 satoshi mined the genesis block thereby launching the bitcoin network and on 9 January 2009 satoshi released the software for public use.
So concluding that today is the creation of genesis block/ the launch of bitcoin network and August 22, 2008 was the real birth of E-Cash which was known only to Wei Dai back then.