From SN 15.4:
“Mendicants, transmigration has no known beginning. No first point is
found of sentient beings roaming and transmigrating, hindered by
ignorance and fettered by craving.
What do you think? Which is more: the mother’s milk you’ve drunk while
roaming and transmigrating for such a very long time, or the water in
the four oceans?”
“As we understand the Buddha’s teaching, the mother’s milk we’ve drunk
while roaming and transmigrating is more than the water in the four
“Good, good, mendicants! It’s good that you understand my teaching
like this. The mother’s milk you’ve drunk while roaming and
transmigrating for such a very long time is more than the water in the
Why is that? Transmigration has no known beginning. … This is quite
enough for you to become disillusioned, dispassionate, and freed
regarding all conditions.”
According to the sutta above, you have been reborn for more times than you can count, with no known beginning to suffering.
Usually, people take this to mean that the very same consciousness that is reading this answer has been reborn many times and experienced all that has been experienced through this body since birth.
However, according to MN 38, this is not true:
The Blessed One then asked him: “Sāti, is it true that the following
pernicious view has arisen in you: ‘As I understand the Dhamma taught
by the Blessed One, it is this same consciousness that runs and
wanders through the round of rebirths, not another’?”
“Exactly so, venerable sir. As I understand the Dhamma taught by the
Blessed One, it is this same consciousness that runs and wanders
through the round of rebirths, not another.”
“What is that consciousness, Sāti?”
“Venerable sir, it is that which speaks and feels and experiences here
and there the result of good and bad actions.”
“Misguided man, to whom have you ever known me to teach the Dhamma in
that way? Misguided man, have I not stated in many ways consciousness
to be dependently arisen, since without a condition there is no
origination of consciousness? But you, misguided man, have
misrepresented us by your wrong grasp and injured yourself and stored
up much demerit; for this will lead to your harm and suffering for a
Consciousness is always changing and it is dependently originated. However, it may appear to be the same just as the water stream of a river appears to be the same, when in fact, the droplets of water in it are constantly changing. Please see this answer.
So, yes - you have been reborn for an uncountable number of times and have drunk more mother's milk than the waters of the four oceans. But who are "you"? You are not the same consciousness that moves through the births.
"You" refers to the self i.e. the thought or idea of the self. It's not a soul. It's simply the thought or idea or view of the self in the mind. It's not the same common self for every person. It's also not the same thought that exists at all moments in time - it's dependently originated.
When there is the thought of the self, there is the objectification and classification (papanca) of everything else that is perceived as non-self, relative to its relationship to the self. This causes the arising of craving and suffering. This is elaborated in this answer.
So, there is definitely rebirth - not the rebirth of a permanent consciousness or soul, but rather the rebirth of the mental idea of the self, and together with it, the rebirth of suffering.
So, the Buddha looks at YOU - yes, that's right - YOU - the SELF - and tells you that you have been reborn for an uncountable number of times, with no known beginning. You (the SELF) have also drunk more mother's milk than the four oceans combined. This to me, is definitely proof that there is rebirth in Buddhism, just not the kind of rebirth that you may have in mind.