I think first it is necessary to understand what Original Sin is/what the Church means by teaching such a thing. Namely, that Original Sin is not personal sin, but is a condition we are born with because of the Fall (we lack sanctifying grace). And the result of Original Sin is death and suffering, concupiscence, and the privation of sanctifying grace (remedied in Sacramental Baptism). If we were not born with Original Sin then we would not die or suffer, because those are consequences of Adam’s Sin (cf. Genesis 3:19).
Now, as to evidence for Original Sin:
Non-Scriptural evidence: look around.
Scriptural evidence:
Genesis 3 (whole chapter) describes the Event (the Fall) from which Original Sin comes.
Romans 5:12-19 “12 Wherefore as by one man sin entered into this world, and by sin death; and so death passed upon all men, in whom all have sinned. 13 For until the law sin was in the world; but sin was not imputed, when the law was not. 14 But death reigned from Adam unto Moses, even over them also who have not sinned after the similitude of the transgression of Adam, who is a figure of him who was to come. 15 But not as the offence, so also the gift. For if by the offence of one, many died; much more the grace of God, and the gift, by the grace of one man, Jesus Christ, hath abounded unto many16 And not as it was by one sin, so also is the gift. For judgment indeed was by one unto condemnation; but grace is of many offences, unto justification. 17 For if by one man’s offence death reigned through one; much more they who receive abundance of grace, and of the gift, and of justice, shall reign in life through one, Jesus Christ. 18 Therefore, as by the offence of one, unto all men to condemnation; so also by the justice of one, unto all men to justification of life. 19 For as by the disobedience of one man, many were made sinners; so also by the obedience of one, many shall be made just.”
1 Corinthians 5:21-22 “21 For by a man came death, and by a man the resurrection of the dead. 22 And as in Adam all die, so also in Christ all shall be made alive.”
Ephesians 2:1-5 “1 And you, when you were dead in your offences, and sins, 2 Wherein in time past you walked according to the course of this world, according to the prince of the power of this air, of the spirit that now worketh on the children of unbelief: 3 In which also we all conversed in time past, in the desires of our flesh, fulfilling the will of the flesh and of our thoughts, and were by nature children of wrath, even as the rest: 4 But God, (who is rich in mercy,) for his exceeding charity wherewith he loved us, 5 Even when we were dead in sins, hath quickened us together in Christ, (by whose grace you are saved,)”