Super Saiyan Infinity: Dragon Ball Will NEVER Allow Goku's Ultimate Final Form
Prior to "Dragon Ball Z: Battle of Gods" kicking off the "Dragon Ball Super" era in 2013, Goku's power maxed out at either Super Saiyan 3 or Super Saiyan 4 depending on whether or not "Dragon Ball GT" can be considered canon. A few years into "Super," however, Goku surpassed even the perhaps non-canonical Super Saiyan 4 form, attaining a transformation called Super Saiyan God Super Saiyan — or Super Saiyan Blue — before learning the even more powerful Ultra Instinct ability.
While Ultra Instinct Goku is magnitudes stronger than most fictional characters, some fans of the "Dragon Ball" franchise have, unsurprisingly, invented a transformation called Super Saiyan Infinity that's far more powerful, even, than Goku's strongest canonical form to date.
One characterization of Super Saiyan Infinity on the Ultra Dragon Ball Wiki, which is dedicated to fan-made "Dragon Ball" content, mentions that it grants Goku infinite stamina and immortality in addition to significant power-ups to his signature attacks. Of course, his hair also becomes so large it envelops his body completely. Another version of the character by YouTube animator Lord Aizen, in a video with more than 20 million views, sports similarly massive hair and a god-like aura. A different fan wiki describes yet another incarnation of the Super Saiyan Infinity concept, proving that the idea remains popular among a subset of the franchise's fanbase. That said, by definition this form is guaranteed to forever remain within the realm of fan content without ever crossing over into "Dragon Ball" canon.
Goku must always strive for more strength and can never become infinitely powerful
One of Goku's defining characteristics is his insistence on constantly training to become stronger. This obsession inspires him to frequently spare villains their lives, not necessarily showing them empathy but merely guaranteeing that he'll retain a rival who can motivate him to train harder. As a result, Goku is constantly learning new power-ups like Super Saiyan Blue and Ultra Instinct. And it's because of this central component of his character that numerous fans have synchronously come up with Super Saiyan Infinity.
However, this is also why Super Saiyan Infinity is contrary to the "Dragon Ball" franchise's very nature. Since Super Saiyan Infinity is intended to be the strongest possible version of Goku, learning this or an equivalent ability would nullify Goku's core personality trait. While theoretically such a technique might make for a fitting conclusion for "Dragon Ball," at the end of "Dragon Ball Z" he looks forward to a young boy with massive potential named Uub becoming a powerful fighter, making it clear that he's happiest not when he's the strongest in the universe but when he has someone pushing him to grow.
If Goku does ever attain Super Saiyan Infinity though, as Reddit commenter GhoulArtist pointed out in a thread about Lord Aizen's YouTube video, he could always still always aim for the even more powerful Super Saiyan Infinity Plus One.