Yes, Genesis 3:15 is the first indication of Our Lady's Immaculate Conception. The doctrine, however, cannot be proven from Scripture. Passages like Genesis 3:15, rather, give us clue.
The Immaculate Conception is the teaching from God's Sacred Oral Tradition. No one on the European continent doubted the doctrine before the 12th century. Eventually, to settle the issue the Pope declared the dogma in 1854.
Proof from Scripture
Genesis 3:15
No direct or categorical and stringent proof of the dogma can be brought forward from Scripture. But the first scriptural passage which contains the promise of the redemption, mentions also the Mother of the Redeemer. The sentence against the first parents was accompanied by the Earliest Gospel (Proto-evangelium), which put enmity between the serpent and the woman: "and I will put enmity between thee and the woman and her seed; she (he) shall crush thy head and thou shalt lie in wait for her (his) heel" (Genesis 3:15). The translation "she" of the Vulgate is interpretative; it originated after the fourth century, and cannot be defended critically. The conqueror from the seed of the woman, who should crush the serpent's head, is Christ; the woman at enmity with the serpent is Mary. God puts enmity between her and Satan in the same manner and measure, as there is enmity between Christ and the seed of the serpent. Mary was ever to be in that exalted state of soul which the serpent had destroyed in man, i.e. in sanctifying grace. Only the continual union of Mary with grace explains sufficiently the enmity between her and Satan. The Proto-evangelium, therefore, in the original text contains a direct promise of the Redeemer, and in conjunction therewith the manifestation of the masterpiece of His Redemption, the perfect preservation of His virginal Mother from original sin.
Luke 1:28
The salutation of the angel Gabriel — chaire kecharitomene, Hail, full of grace (Luke 1:28) indicates a unique abundance of grace, a supernatural, godlike state of soul, which finds its explanation only in the Immaculate Conception of Mary. But the term kecharitomene (full of grace) serves only as an illustration, not as a proof of the dogma.
Other texts
From the texts Proverbs 8 and Ecclesiasticus 24 (which exalt the Wisdom of God and which in the liturgy are applied to Mary, the most beautiful work of God's Wisdom), or from the Canticle of Canticles (4:7, "Thou art all fair, O my love, and there is not a spot in thee"), no theological conclusion can be drawn. These passages, applied to the Mother of God, may be readily understood by those who know the privilege of Mary, but do not avail to prove the doctrine dogmatically, and are therefore omitted from the Constitution "Ineffabilis Deus". For the theologian it is a matter of conscience not to take an extreme position by applying to a creature texts which might imply the prerogatives of God.
Proof from Tradition
In regard to the sinlessness of Mary the older Fathers are very cautious: some of them even seem to have been in error on this matter.
* Origen, although he ascribed to Mary high spiritual prerogatives, thought that, at the time of Christ's passion, the sword of disbelief pierced Mary's soul; that she was struck by the poniard of doubt; and that for her sins also Christ died (Origen, "In Luc. hom. xvii").
* In the same manner St. Basil writes in the fourth century: he sees in the sword, of which Simeon speaks, the doubt which pierced Mary's soul (Epistle 259).
* St. Chrysostom accuses her of ambition, and of putting herself forward unduly when she sought to speak to Jesus at Capharnaum (Matthew 12:46; Chrysostom, Homily 44 on Matthew).
But these stray private opinions merely serve to show that theology is a progressive science. If we were to attempt to set forth the full doctrine of the Fathers on the sanctity of the Blessed Virgin, which includes particularly the implicit belief in the immaculateness of her conception, we should be forced to transcribe a multitude of passages. In the testimony of the Fathers two points are insisted upon: her absolute purity and her position as the second Eve (cf. 1 Corinthians 15:22).
Mary as the second Eve
This celebrated comparison between Eve, while yet immaculate and incorrupt — that is to say, not subject to original sin — and the Blessed Virgin is developed by:
* Justin (Dialogue with Trypho 100),
* Irenaeus (Against Heresies III.22.4),
* Tertullian (On the Flesh of Christ 17),
* Julius Firmicus Maternus (De errore profan. relig xxvi),
* Cyril of Jerusalem (Catecheses 12.29),
* Epiphanius (Hæres., lxxviii, 18),
* Theodotus of Ancyra (Or. in S. Deip n. 11), and
* Sedulius (Carmen paschale, II, 28).
The absolute purity of Mary
Patristic writings on Mary's purity abound.
* The Fathers call Mary the tabernacle exempt from defilement and corruption (Hippolytus, "Ontt. in illud, Dominus pascit me");
* Origen calls her worthy of God, immaculate of the immaculate, most complete sanctity, perfect justice, neither deceived by the persuasion of the serpent, nor infected with his poisonous breathings ("Hom. i in diversa");
* Ambrose says she is incorrupt, a virgin immune through grace from every stain of sin ("Sermo xxii in Ps. cxviii);
* Maximus of Turin calls her a dwelling fit for Christ, not because of her habit of body, but because of original grace ("Nom. viii de Natali Domini");
* Theodotus of Ancyra terms her a virgin innocent, without spot, void of culpability, holy in body and in soul, a lily springing among thorns, untaught the ills of Eve, nor was there any communion in her of light with darkness, and, when not yet born, she was consecrated to God ("Orat. in S. Dei Genitr.").
* In refuting Pelagius St. Augustine declares that all the just have truly known of sin "except the Holy Virgin Mary, of whom, for the honour of the Lord, I will have no question whatever where sin is concerned" (On Nature and Grace 36).
* Mary was pledged to Christ (Peter Chrysologus, "Sermo cxl de Annunt. B.M.V.");
* it is evident and notorious that she was pure from eternity, exempt from every defect (Typicon S. Sabae);
* she was formed without any stain (St. Proclus, "Laudatio in S. Dei Gen. ort.", I, 3);
* she was created in a condition more sublime and glorious than all other natures (Theodorus of Jerusalem in Mansi, XII, 1140);
* when the Virgin Mother of God was to be born of Anne, nature did not dare to anticipate the germ of grace, but remained devoid of fruit (John Damascene, "Hom. i in B. V. Nativ.", ii).
* The Syrian Fathers never tire of extolling the sinlessness of Mary. St. Ephraem considers no terms of eulogy too high to describe the excellence of Mary's grace and sanctity: "Most holy Lady, Mother of God, alone most pure in soul and body, alone exceeding all perfection of purity ...., alone made in thy entirety the home of all the graces of the Most Holy Spirit, and hence exceeding beyond all compare even the angelic virtues in purity and sanctity of soul and body . . . . my Lady most holy, all-pure, all-immaculate, all-stainless, all-undefiled, all-incorrupt, all-inviolate spotless robe of Him Who clothes Himself with light as with a garment . . . flower unfading, purple woven by God, alone most immaculate" ("Precationes ad Deiparam" in Opp. Graec. Lat., III, 524-37).
* To St. Ephraem she was as innocent as Eve before her fall, a virgin most estranged from every stain of sin, more holy than the Seraphim, the sealed fountain of the Holy Ghost, the pure seed of God, ever in body and in mind intact and immaculate ("Carmina Nisibena").
* Jacob of Sarug says that "the very fact that God has elected her proves that none was ever holier than Mary; if any stain had disfigured her soul, if any other virgin had been purer and holier, God would have selected her and rejected Mary". It seems, however, that Jacob of Sarug, if he had any clear idea of the doctrine of sin, held that Mary was perfectly pure from original sin ("the sentence against Adam and Eve") at the Annunciation.
St. John Damascene (Or. i Nativ. Deip., n. 2) esteems the supernatural influence of God at the generation of Mary to be so comprehensive that he extends it also to her parents. He says of them that, during the generation, they were filled and purified by the Holy Ghost, and freed from sexual concupiscence. Consequently according to the Damascene, even the human element of her origin, the material of which she was formed, was pure and holy. This opinion of an immaculate active generation and the sanctity of the "conceptio carnis" was taken up by some Western authors; it was put forward by Petrus Comestor in his treatise against St. Bernard and by others. Some writers even taught that Mary was born of a virgin and that she was conceived in a miraculous manner when Joachim and Anne met at the golden gate of the temple (Trombelli, "Mari SS. Vita", Sect. V, ii, 8; Summa aurea, II, 948. Cf. also the "Revelations" of Catherine Emmerich which contain the entire apocryphal legend of the miraculous conception of Mary.
From this summary it appears that the belief in Mary's immunity from sin in her conception was prevalent amongst the Fathers, especially those of the Greek Church. The rhetorical character, however, of many of these and similar passages prevents us from laying too much stress on them, and interpreting them in a strictly literal sense. The Greek Fathers never formally or explicitly discussed the question of the Immaculate Conception.