Obviously, Paul McCartney wants Blackbird to be interpreted as a "Black Woman". "Bird" is a British Idiom for "Woman", but it is offensive, so the song is not using this connotation.

The Dead of Night - In the 60's the Doomsday Clock was, as it still is, set at near midnight. 

Blackbird has other connotations of "Poet" in Irish Literature and Archetypes, of a Rebel Poet. Though, it's unlikely Paul McCartney is singing about poets, though, he could also be referencing Audre Lorde who published her first volume of poetry that same year. The White Album was published in Late November of 1968. So it might be a reference.

However, the Blackbird of Irish Poetry was a rebel poet who was persecuted for their songs; some were hung for their poems, while others were thrown into prison. The song might also be, unintentionally, a criticism of the censorship of black voices. The work could be claiming, though likely not intended by its author, there's a victory of the "Blackbird" to overcome censorship and Racial Boundaries. 

"All your life, you were only waiting for this moment to arise." The moment being the expansion of Civil Rights in 1968. There was a significant expansion of Civil Rights in 1968.

1968, the same year The Beatles published the White Album, there were many advances for Free Speech and Civil Rights. The Blackbird having its historical significance of a rebel poet martyred for their speech (Unlikely intentioned by the Song's Creator), and its literal interpretation given by Paul McCartney of a "Black Woman". 

One could almost assume it to be Audre Lorde whom the poem refers to, if not literally then symbolically, and her publication of "The First Cities".

Beatles, The. The White Album. Apple Records, 1968. YouTube.