Disclaimer - this is a purely speculative post and does not aim to offend followers or believers of any particular faith or religion.
Hinduism, as it stands today, is defined by the the Vedas, the Upanishads, the Puranas, the Ramayana and the Mahabharata primarily. As one compares and contrasts Hinduism with the modern religions like Christianity or Islam, one fundamental idea presents itself as a stark difference - the idea of rebirth. Modern religions believe that we actually live only once (go YOLO!), residing for all eternity in Heaven or Hell in the afterlife based on our actions, thoughts, sins, guilt and what not during the time spent living. Hinduism, on the other hand, postulates that the soul is immortal and caught in a cycle of rebirths till one attains nirvana or moksha by elevating one's consciousness and merging into the infinite. The same applies to Jainism and Buddhism too, where Moksha or Nirvana are the end goal.
Now, there is no scientific evidence (as far as I know) to support either of these views as yet, though there are multiple claims of people experiencing both these phenomena. But, come to think of it, the concept of multiverse actually can be attributed to the concept of rebirth. Of course, the similarity is not straightforward or forthcoming. But I assume you would indulge me somewhat.
Let us start with the concept of the multiverse for the uninitiated. Scientists have long theorized that ours is not the only universe that exists. It is theorized that there exist an infinite number of universes, each slightly different from the other yet similar, existing in higher dimensions unobservable to human senses and capabilities. Each universe contains a replica of everything in the other universe albeit different due to the different choices made by someone. So, probably, there is another universe where I didn't write this piece, another one where you did not read this and so on. Imagine all the possible combinations of the sum total of choices made by every conscious being since the advent of time itself - those are the number of parallel universes that exist!
That alone, although necessary, will not suffice the need of what could possibly be the scientific basis of rebirth. For that, another rather inexplicable phenomenon named quantum entanglement needs to be thrown into the mix. Quantum entanglement suggests that in certain scenarios, two particles can be linked together in such an exotic way that information exchange between them is instantaneous depsite the distance between them. There is a sort of cause-effect relationship between the two entities in the quantum realm, the observation or measurements on one particle instantly affecting the measurements on the entangled particle. And this is not a science fiction movie where the term "quantum"-something is thrown around just to avoid explaining the science behind what is going to happen.
With these two concepts in mind, the next item to analyze is the concept of the aatma and it's rebirth. Hinduism is rooted in the idea that the aatma is caught in loop if rebirths (talk about Tom Cruise fighting aliens in a loop!), moving from one vessel (body) to another and that our current life is affected by what we did in the past lives, and what we do in this life affects our future lives. Whatever knowledge we gained in previous lives is not forgotten, whatever good we did, or the bad we did, is not forgotten; it is just hidden or obscured due to our worldly sensory deprivation. Our life is the summation of all the lives we have lived and will live. However, all of this assumes that the arrow of time actually exists, that there is a "previous" and a "next" life. That is true for three dimensional beings (for example, humans), but for residents of higher dimensions, there is no arrow of time, there is no past and no future, no previous and no next. For higher dimensional beings, every moment is accessible simultaneously, just like the three dimensions humans can experience.
An amalgamation of all these concepts presents a highly unlikely yet plausible answer to the rebirth theory. Assuming that enlightened beings probably see higher dimensions and perceive time non-linearly, if we take the arrow of time out of the equation from the concept of rebirth, it simplifies rebirth down to - a being experiencing multiple lives in parallel, simultaneously. Since the theory of multiverse suggests that each of us are living multiple lives in parallel universes, that does not seem to be a far fetched idea at all. Also, the idea that what we do in one life impacts the other is also not far fetched if quantum entanglement exists - all replicas of a being in parallel universes could possibly be connected via quantum entanglement, leading to a cyclic cause-effect relationship of karma as defined in Hinduism.
What does all of this mean, you ask? In simpler words, probably, it means that what a being does in this life, in this instant, in this universe impacts the life of one's replica in every other existing parallel universe. An axiom to that - it also means that one's current situation, the outcomes of past, current and future events and everything else conveniently attributed to fate or destiny is nothing more than the impact of the actions of one's replicas from other universes. There is a shared subconsciousness connecting all the replicas of a being across all universes, connecting them through quantum entanglement, exchanging information on actions, thoughts, ideas, knowledge and much more across universes instantaneously.
As a by-product of this thought, probably 84 lakh (8,400,000) yonis actually point to the existence of 8.4 million parallel universes. Who knows? The scribes who wrote the scriptures were bound by their human potential, while the source of the scriptures were mostly omniscient beings who could perceive higher dimensions and understood the quantum realms. Discourses like the Gita were meant to be simple so that humans could grasp it despite the limited consciousness and universal awareness. Or, probably, it is just the musings of a curious mind.
