The Lord of the Rings sees the burden of the One Ring land on Frodo after multiple millenniums of being lost. As soon as he leaves the Shire with the Ring, it seems like Sauron and his minions are hot on his trail up until the very end. So, if Sauron could locate the Ring so quickly, how come he didn't find it as it sat in a river for over 2000 years?
As seen in the opening of The Lord of the Rings: The Fellowship of the Ring, Isildur was corrupted by the One Ring and took it for himself. Eventually, orcs ambushed him, and he wore the Ring as he fled into a nearby river. The One Ring decided to abandon Isildur, and the orcs shot him dead. It was here, along the Anduin, that the Ring was lost for over two and a half thousand years until Déagol and Smeagol discovered it.
Not only was the Ring in the Anduin for a long time, but its location wasn't all that far from Mordor. Then, after Smeagol found the Ring, he sat in the Misty Mountains for over 500 years as it corrupted him. With all this time, it seems Sauron would have found the Ring. However, the simplest as to why he didn't: Sauron had no way of locating his Ring.
Because the Nazgûl track Frodo, and the Eye of Sauron "sees" him when he wears the Ring, some presume that Sauron has some way of tracking it. However, this is not the case and proven when Frodo crossed into Mordor and entered Mount Doom without Sauron ever realizing. So, as the One Ring sat at the bottom of the river, Sauron had no clue as to its whereabouts and no way of finding it.
The only way the Nazgûl were able to locate the Ring so easily is because of Smeagol, aka Gollum, who was tortured and gave them the words "Shire" and "Baggins." From then on, there was a lot of tracking and guesswork from Sauron and his Nazgûl as to where his Ring was in Middle-earth. Sauron eventually assumed Aragorn had the Ring as he attacked the Black Gate, which gave Sam and Frodo the perfect distraction.
Knowing Sauron couldn't track the One Ring, it's logical to think about simply burying it underground or deep in the ocean. This idea was brought up to Gandalf in the books, who explains that while it may give temporary peace, the Ring would inevitably be found by some kind of creature. Also, Sauron doesn't need his Ring to still be a threat. Therefore, it's arguable that he still could've taken over Middle-earth; it just would've been more of a struggle.