Although St. Augustine clearly tops the list (at least in the West) of those Church Fathers who taught the doctrine of Original Sin, he surely is not the first.
First off, lets define Original Sin:
Original sin, also called ancestral sin, is the Christian doctrine of
humanity's state of sin resulting from the fall of man, stemming from
Adam's rebellion in Eden. (Wikipedia)
Original Sin is arguably the most touched upon doctrine in the history of the Church - not counting Sacred Scripture (which wasn't clearly agreed upon for the first 3 centuries) - simply because its the root cause of our need for salvation.
Reference: Gen 3; 1 Cor 15:21; Rom 5:12,15; 6:23; Rom 5:12,19; Psalm 51:5; Eph 2:1-3
Discussion of this doctrine is clearly evident in the early centuries of the Church.
St. Irenaeus writes toward the end of the 100's:
....having become disobedient, [Eve] was made the cause of death for
herself and for the whole human race; so also Mary, betrothed to a man
but nevertheless still a virgin, being obedient, was made the cause of
salvation for herself and for the whole human race....Thus, the knot
of Eve's disobedience was loosed by the obedience of Mary. What the
virgin Eve had bound in unbelief, the Virgin Mary loosed through
faith. ...But this man [of whom I have been speaking] is Adam, if
truth be told, the first-formed man....We, however, are all
from him; and as we are from him, we have inherited his title [of sin]. ...Indeed, through the first Adam, we offended God by not observing His command. Through the
second Adam, however, we are reconciled, and are made obedient even
unto death. For we were debtors to none other except to Him, whose
commandment we transgressed at the beginning. (Against Heresies
3:22:4; 3:23:2; 5:16:3 emphasis mine)
Later we find Tertullian (c. 200 AD)
Finally, in every instance of vexation, contempt, and abhorrence, you
pronounce the name of Satan. He it is whom we call the angel of
wickedness, the author of every error, the corrupter of the whole
world, through whom Man was deceived in the very beginning so that he
transgressed the command of God. On account of his transgression Man
was given over to death; and the whole human race, which was infected
by his seed, was made the transmitter of condemnation. (The Testmiony
of the Soul 3:2, c. 200 AD)
Origin (c. 244 AD):
Every soul that is born into flesh is soiled by the filth of wickedness and sin....And if it should seem necessary to do so,
there may be added to the aforementioned considerations [referring to
previous Scriptures cited that we all sin] the fact that in the
Church, Baptism is given for the remission of sin; and according to
the usage of the Church, Baptism is given even to infants. And indeed
if there were nothing in infants which required a remission of sins
and nothing in them pertinent to forgiveness, the grace of Baptism
would seem superfluous. (Homilies on Leviticus 8:3)
The Church received from the Apostles the tradition of giving Baptism
even to infants. For the Apostles, to whom were committed the secrets
of divine mysteries, knew that there is in everyone the innate
stains of sin, which must be washed away through water and the
Spirit. [cf. John 3:5; Acts 2:38]. (Commentaries on Romans 5:9)
St. Cyprian of Carthage (c. 250 AD):
If, in the case of the worst sinners and of those who formerly sinned
much against God, when afterwards they believe, the remission of their
sins is granted and no one is held back from Baptism and grace, how
much more, then, should an infant not be held back, who, having but
recently been born, has done no sin [committed no personal sin],
except that, born of the flesh according to Adam, he has contracted
the contagion of that old Death from his first being born. (Letters
64:5 of Cyprian and his 66 colleagues in Council to Fidus)
There are dozens more writings from early Church Fathers.
Long story short...
Despite the fact that Augustine is perhaps the most referenced theological giant (in the West at least), he most certainly isn't the first.