The Online Etymology Dictionary says sustainability is from 1972, though its root words are much older.
sustainable
1610s, "bearable," from sustain + -able. Attested
from 1845 in the sense "defensible;" from 1965 with the meaning
"capable of being continued at a certain level." Sustainable growth is
recorded from 1965. Related: Sustainability (1972).
An article by Nathan Thanki called Sustainable: a philological investigation gives some background, here's an excerpt that neatly links sustainability with Nachhaltigkeit:
So it is what we are trying to sustain that is usually the meat of
arguments about “sustainability”—is it overconsumption,
overpopulation, environmental degradation? The term has become
synonymous with that “meat” in the past few decades. The Club of Rome,
in its 1972 report, “Limits to Growth,” claimed that it was searching
for a global equilibrium, “a world system that is: 1. sustainable
without sudden and uncontrolled collapse; and 2. capable of satisfying
the basic material requirements of all of its people.” When the World
Commission on Environment and Development (aka the Brundtland
Commission) concluded with the notion of “sustainable development,”
the emergence of the concept we know too well today was fully
underway. Since that time, sustainability has come to be almost
synonymous with “sustainable development, defined in Our Common Future
as “development that meets the needs of the present without
compromising the ability of future generations to meet their own
needs.”
...
While the origins of the words association with the environmental seem
to lie in the emergence of the environmental movement of the 70s,
Ulrich Grober points out a deeper root. In “A conceptual history of
‘sustainable development’ (Nachhaltigkeit),” he argues that the term
actually comes from 18th Century forestry (at the time timber was a
key resource with an uncertain future). German nobleman and forester
Hans Carl von Carlowitz wrote “’daß es eine continuirliche beständige
und nachhal–tende Nutzung gebe,’ (that there would be a continuous,
steady and sustained use).” Sadly, Europe no longer has any primeval
forest outside of the Białowieża Forest in Poland and Belarus.So it
would appear to me that the quest for “sustainability” is older than
we commonly recognise, and, thus, so is our failure to achieve it:
marking the failure of civilization.
Edit: The 1972 date is surprisingly late, here are some antecedents from 1906 and 1907.