That's a good question. It took me a long time to come to this realization so there isn't any one thing that I can point to, but I tried to summarize my thoughts on the matter as best I could. Be warned that there is a lot of junk "science" out there. If you research this, try to stay away from anything that sounds too fantastical. No one knows anything about this as fact, not even me. These are just my observations and conclusions, but I think it's important to keep an open mind on these matters and pursue further research into the topic.

1. Carl Jung theorized about a "Collective Unconsciousness" that all of humanity shares. He noticed that completely separated cultures tended to have the same thoughts at the same time. Around the same time the ancient Chinese were dreaming up dragons, so too were the europeans despite not having any contact with each other. Many religions share the same stories, like The Flood. I theorize that humans in fact share some sort of "soul" from which the individual is born. The collective unconsciousness is a fragment of that "shared soul". https://www.britannica.com/science/collective-unconscious

2. Joseph Campbell developed the "monomyth" or the story of The Hero With A Thousand Faces. Dr. Campbell noted that accross all cultures, across all time, humans tend to tell the same generalized story of a nobody that is born nowhere special that receives a call to adventure. They gain a mentor and learn to control a supernatural power. They go on to face temptations and challenges, have a revelation about reality, transform, atone for past sins, defeat the ultimate evil and ride off into the sunset (I'm generalizing here for simplicity). Over and over and over humans tell this story. Beowulf, Tangled, The Hunger Games, Star Wars, Harry Potter, The Wheel of Time, Moana, Theseus, Odysseus, Jesus Christ, Krishna of Hindu belief, Spiderman, and on and on. The Monomyth does not specifically address reincarnation, however I posit that this cycle is not just a coincidence, but a fundamental aspect of human life. We are telling the story of how we reincarnate over and over and face and overcome lifes challenges. https://en.wikipedia.org/wiki/Hero%27s_journey

3. More recently, Dr. Ian Stevenson and Dr. Jim Tucker have used the scientific method to exaustively study chidren who claim to remember details from a past life. When presented with such a child, they did their best to discredit the child and determine how the child could have learned their knowledge through regular, non-spiritual means (listening to the radio, watching TV, reading old letters, etc.). Their research is iron clad and has not been discredited yet, and has been subject to lots of scrutiny. What they ended up with was about 2,000 cases of children who seemingly remember details from past lives that they couldn't possibly have learned in this life. It is fascinating research. Neither doctor has explicitly stated that reincarnation is definitely real, but they have both examined the evidence and believe that it merrits yet further research. https://www.psychologytoday.com/us/blog/out-the-darkness/202112/evaluating-the-evidence-reincarnation

Lastly, your specific subjective experience means that it is possible for the universe to form you specifically from basically nothing. The only evidence you need to prove this fact is your own mind (I think, therefore I am). The specific mechanisms of this formation aren't actually important and I won't pretend to know what they are. If "you" can form once, is it so absurd to believe that it could happen twice? If twice, why not an infinite number of times?