As a transmigrant from another world, Izayoi views everything from a higher narrative level—definitely above anyone else on this planet.
A thousand years have passed. Many people now believe that the Sage of Six Paths and the Ninja Creed are just myths and legends. But Izayoi knows they're real. He also knows the Sage of Six Paths had a mother, as well as a younger brother. After the two brothers joined forces to seal their mother away, the Sage of Six Paths became the Ten-Tails Jinchuriki and embarked on a journey of atonement, while Otsutsuki Hamura married, had children, and built up his family line.
Once the Sage of Six Paths was no longer the Ten-Tails Jinchuriki, he left the husk of the Ten-Tails—the Gedo Statue—on the moon. To guard it, Otsutsuki Hamura took part of the Otsutsuki clan to live on the moon. The branch that stayed on Earth eventually became the Hyuga clan.
Just like how the Sage of Six Paths had the ultimate eye technique, the Rinnegan—and how his two sons, if their polar opposites combined, could awaken the Rinnegan—Otsutsuki Hamura had his own ultimate eye technique: the Tenseigan, which holds both the power to destroy and the power to create. His descendants have a chance to awaken the Tenseigan under conditions similar to those "two opposites becoming one." Unlike the Rinnegan, there's also a secret method to merge large numbers of Byakugan and artificially produce a Tenseigan. This is how the Otsutsuki branch on the moon ended up getting wiped out—except for Toneri Otsutsuki, who's basically the only survivor up there now.
Back when Izayoi was three, it occurred to him that he shouldn't rush to copy Uzumaki Naruto or Uchiha Sasuke's talent entries—he suddenly thought of Toneri Otsutsuki. As a descendant of the moon's branch family, Toneri carries a purely Otsutsuki bloodline, on par with ancient figures like Asura and Hagoromo Otsutsuki. Because of that pure lineage, Toneri naturally has the sort of "Sage Body" talent.
When Uchiha Madara merged Senju Hashirama's cells into himself, he only awakened the Rinnegan at the end of his life. But Toneri only needed a few days to evolve his Byakugan into the Tenseigan. The moment it awakened, he could enter Tenseigan Chakra Mode, form chakra orbs, and unleash both Silver Wheel Reincarnation Explosion and the Golden Wheel Reincarnation Explosion that sliced the moon apart. His natural gifts and chakra reserves are downright extreme—way above even Naruto and Sasuke. If Toneri ever moved down to Earth, he would be the most broken character of his era. If he brought the giant Tenseigan with him, then unless Madara and Hashirama both came back to life, or the Sage of Six Paths personally stepped in, the ninja world would have to do things his way.
If he were especially ruthless and stole Hinata's or Hanabi's Byakugan early on, there wouldn't be any "Shippuden," just "Toneri's Legend." Unfortunately for him (or maybe fortunately for everyone else), Toneri is basically a naive shut-in with grand delusions. Unless he's sure the ninja world is beyond saving—or until he's old enough—he won't leave the moon.
Still, Izayoi knows that Toneri did visit Earth and Konoha once in childhood, back when his father was still alive. Using the giant Tenseigan as a remote medium, he secretly saw Hinata. He fell in love with her at first sight, yet never disturbed her life, planning to propose once he was grown. Little did he know his "fiancée" already had someone else she liked. It was all just his own wishful thinking.
Izayoi doesn't really have much to say about that clueless, overdramatic shut-in. But he does guess that Toneri's visit happened when Hinata was three—because right after she turned three, her uncle Hizashi died in Hiashi's place, causing a slight shift in her status. From that point on, her personality changed, and Hiashi basically lost all hope in her. Her biggest birthday party ever was when she turned three.
So Izayoi decided to gamble everything on that moment. He intended to use his one-time-only "copy talent entry" on Toneri Otsutsuki. There would be plenty of chances to pick up Naruto's or Sasuke's talents, but only one shot for Toneri's. Missing it would mean waiting until at least two years after Shippuden ended.
Looking at the info displayed on his mental interface now, it's clear Izayoi's gamble paid off. He didn't just hang around outside the Hyuga compound on Hinata's third birthday—he spent a whole year prowling around Konoha.
Appearances can fool you, but those floating "talent bubbles" never lie. As long as someone wasn't a puppet or invisible, Izayoi's gift would catch them. Sure enough, during Hinata's third birthday—when the Kumo envoy also visited Konoha—Izayoi spotted a blind Toneri and his father in the crowd.
It's worth noting: the Kumo delegation got lucky. If Toneri and his father had stayed until nightfall and tried to kidnap Hinata themselves, they'd have ended the story right then and there. But father and son only used the giant Tenseigan from afar to get a glimpse of Hinata—who hadn't joined the festivities but was celebrating inside the Hyuga compound—and then left Konoha.
Toneri, who was born without eyes, didn't have a "Kekkei Genkai: Byakugan" talent entry—or any lower-tier entries for that matter. The only thing showing up on him was a grand, red-colored bubble labeled Otsutsuki Bloodline.
Izayoi had seen "Otsutsuki Bloodline" on various Hyuga clan members before, but theirs only went as high as Blue. Even Toneri's father had a "Purple"-tier Otsutsuki Bloodline, not even Gold. But Toneri's version was a tier above Gold, that is, Red—the highest Izayoi had discovered so far. He didn't hesitate for a second and copied that entry on the spot.
Over the following three years, Izayoi started rewriting his fate. As soon as he successfully extracted chakra for the first time, his original Chunin Aptitude (Green) talent upgraded straight to Super-Kage Aptitude (Gold)—meaning that, barring an untimely death, he was guaranteed to reach the same level as Hashirama Senju and Madara Uchiha. And if he ever transplanted a Byakugan from Hinata or Hanabi and formed Truth-Seeking Orbs, he'd reach the Six Paths tier.
A few months later, Izayoi unlocked a new talent: All-Attribute Constitution (Purple). Turns out he's just like Tobirama Senju, Hiruzen Sarutobi, Orochimaru, and Kakashi Hatake—able to handle all five basic chakra natures.
At five, Izayoi triggered yet another new entry—and it really gave him a scare.
Because…he activated the Byakugan!
Yep, "activated" it, not "transformed his eyes into" Byakugan. Under the influence of his Otsutsuki bloodline, Izayoi's eyes are normally just like anyone else's—only when he "turns on" the Byakugan do the veins pop at his temples and his pupils go white, much like Himawari Uzumaki's.
He breathed a huge sigh of relief. If his eyes had become permanently white, he'd be stuck wearing sunglasses 24/7 or pulling a Kakashi and disguising himself under colored contacts.