This question about Avatarhood and his previous lives if any is taken up by Sri Aurobindo himself in Essays on the Gita, as cited below.
‘The question then arises, and it is the sole real difficulty, for here the intellect falters and stumbles over its own limits, how is this human mind and body assumed? For they were not created suddenly and all of a piece, but by some kind of evolution, physical or spiritual or both. No doubt, the descent of the Avatar, like the divine birth from the other side, is essentially a spiritual B.G.4.6 phenomenon, as is shown by the Gita’s ฤtmฤnaแน sแนjฤmi, it is a soul-birth; but still there is here an attendant physical birth. How then were this human mind and body of the Avatar created? If we suppose that the body is always created by the hereditary evolution, by inconscient Nature and its immanent Life-spirit without the intervention of the individual soul, the matter becomes simple. A physical and mental body is prepared fit for the divine incarnation by a pure or great heredity and the descending Godhead takes possession of it. But the Gita in this very passage applies the doctrine of reincarnation, boldly enough, to the Avatar himself, and in the usual theory of reincarnation the reincarnating soul by its past spiritual and psychological evolution itself determines and in a way prepares its own mental and physical body. The soul prepares its own body, the body is not prepared for it without any reference to the soul. Are we then to suppose an eternal or continual Avatar himself evolving, we might say, his own fit mental and physical body according to the needs and pace of the human evolution and so appearing from age to age, yuge yuge? In some such spirit some would interpret the ten incarnations of Vishnu, first in animal forms, then in the animal man, then in the dwarf man-soul, Vamana, the violent Asuric man, Rama of the axe, the divinely-natured man, a greater Rama, the awakened spiritual man, Buddha, and, preceding him in time, but final in place, the complete divine manhood, Krishna,โfor the last Avatar, Kalki, only accomplishes the work Krishna began,โhe fulfils in power the great struggle which the previous Avatars prepared in all its potentialities. It is a difficult assumption to our modern mentality, but the language of the Gita seems to demand it. Or, since the Gita does not expressly solve the problem, we may solve it in some other way of our own, as that the body is prepared by the Jiva but assumed from birth by the Godhead or that it is prepared by one of the four Manus, B.G.10.6 catvฤro manavaแธฅ, of the Gita, the spiritual Fathers of every human mind and body. This is going far into the mystic field from which the modern reason is still averse; but once we admit Avatarhood, we have already entered into it and, once entered, may as well tread in it with firm footsteps.’
(Ref. https://incarnateword.in/cwsa/19/the-process-of-avatarhood#p11)
The difficulty arises because Sri Krishna, the only Avatar who speaks of it as among the great spiritual secrets, himself says that Arjun and himself have both been born earlier. One may assume that his earlier births were as Vibhutis. Even here, on the battlefield, he declares himself at once as an Avatar as well as a Vibhuti. While describing the various Vibhutis, he includes himself, Krishna among the Vrishnis. One is reminded of Nagin Doshi’s question to Sri Aurobindo along similar lines.
‘Since you and the Mother were on earth constantly from the beginning what was the need for Avataras coming down here one after another?
We were not on earth as Avataras.
You say that you both were not on earth as Avatars and yet you were carrying on the evolution. Since the Divine Himself was on the earth carrying on the evolution, what was the necessity for the coming down of the Avatars who are portions of Himself?
The Avatar is necessary when a special work is to be done and in crises of the evolution. The Avatar is a special manifestation, while for the rest of the time it is the Divine working within the ordinary human limits as a Vibhuti.’
(Ref. https://incarnateword.in/cwsa/32/carrying-on-the-evolution#p24)
It seems that the decision for the succession of Avatars is taken right at the origin of creation itself. Each soul chosen to manifest the Avatarhood at a future point of time goes through the cycle of rebirths preparing it for the necessary experiences until it is ready to assume the full Divine Advent and with it the full burden of Avatarhood. This preparation is necessary since otherwise the sudden descent of the Divine amidst humanity would be quite a disconnected freak event leaving no lasting evolutionary impact except for some stories of miracles. I suppose that is as close as we can get to this deepest of secrets of the Divine Advent in humanity.
Affectionately,
Alok Da
