According to scientific materialism something resembling reincarnation already exists
Think about it - before I was born there was no me, then there was me in my first person perspective. After I die this first person perspective will dissappear and I'll be back to 'square one', back to non-existing just like it was before I was born. It'll be like 'I' never existed in the first place.
Now another person or animal will be born and this person will be a brand new first person perspective just like 'I' was when I was born. In fact it will be 'me' which is not the person writing this post but rather 'first person perspectivity' itself which exists in all conscious creatures. It'll just be me with a different name and physical and mental characteristics. Because there is no immutable 'self' there is just this first person sensation, a sense of self. This self has no owner - it is rather a natural process that occurs.
We didn't win the lottery being born - because anywhere there is consciousness that is us. It doesn't feel like it because the brains and nervous systems of all animals are separated. So the person who is writing this post only has access to the contents of the mind of the person writing this post. If 'my' brain could be merged with someone else's brain the illusion that there are multiple consciousnesses would dissappear.
There is no self - but rather a sensation of self produced by a brain and nervous system (not your brain/nervous system, but rather a brain and nervous system which has no owner and is just a natural process). The sense of self and ownership is just that - it is the brain's model of a human body. It's not your body - but a body with an intense and powerful sensation of 'self' in its brain.
Here's another analogy - imagine there's two people, person A and person B. Person A is then converted and rearranged atom by atom into an exact replica of person B. Then person B is converted and rearanged into an exact replica of person A atom by atom. This includes the physical body and brain even down to memories and the arrangement of neurons. Now tell me - who is who now? Well I'd argue they're both the same person. The same applies to all conscious life.
At the end the day there is a strong and powerful sense of self and a strong sense of familiarity with your world. There is no self, and there is no familiarity, but rather a SENSE of self and familiarity experienced by a brain and body that has no owner, in the same way the sun or the stars has no owner.
Imagine you woke up as a different person this morning along with that person's memory and in their house. Then imagine tomorrow you wake up as another person with different memories. And on and on indefinitely. Then imagine this happens to every life form. Then lets go further and forget waking up or being born as a different person but imagine this 'switch' took place at every momement even when awake. Like my person A and person B analogy but for all life forms. This would even identical to what happens already - if this was or was not happening everything would 'feel' the same as it does now.
Its scary stuff but I've had these intuitions since I was very young, always wondering why am I 'me'. Why has the whole world been seen through my eyes and not someone elses. Answer: I already have seen it and am currently seeing through everyone elses (including animals) eyes I just can't 'rememeber' it because our brains and nervous systems are not connected.