In the very first episode of Yu-Gi-Oh! (the anime), Yugi uses the "Dark Magician" card directly from his hand. This is because at that point in the series, the rules of the game were not yet established and the concept of tribute summoning was not introduced.
The first episode was primarily focused on introducing the characters, the game of Duel Monsters, and the concept of the Millennium Puzzle. It was not until later episodes that the rules of the game were explained in detail, including the concept of tribute summoning.
It's important to remember that the anime's depiction of the game of Duel Monsters wasn't always perfectly consistent with the actual card game. The show took liberties with rules and mechanics for the sake of entertainment.