"as it is written, THERE IS NONE RIGHTEOUS, NOT EVEN ONE;" (a quote from the Psalms)
and Psalm 51, especially verse 5
"Behold, I was brought forth in iniquity, And in sin my mother conceived me."
are generally the first references for the doctrine.
God's reason for destroying the world with water in Genesis via the flood was that "the imaginations of the heart of men are only evil continually".
If there are "none righteous", and we are "brought forth in iniquity", then we have already failed to keep God's holy standard, and are, therefore, depraved from birth. If we are depraved from birth, and we cannot do righteously, then it is throughout the totality of our being.