Bitcoins actual birth date is January 3, 2009, the day Satoshi Nakamoto mined the first block (the genesis block) containing 50 BTC.

Protocol Launch: The first Bitcoin software (v0.1) was released on January 9, 2009, making the network available to the public.
Whitepaper Date: The foundational whitepaper, Bitcoin: A Peer-to-Peer Electronic Cash System, was published on October 31, 2008.
Satoshi’s Birthday: The pseudonymous creator listed his birthday as April 5, 1975, on his P2P Foundation profile; however, this is widely considered symbolic, referencing the anniversary of U.S. Executive Order 6102 (April 5, 1933), and is not his actual birth date.