I'm not just talking about the main series games, the side games like PMD count too.
Of all the Pokémon games I can think of, the earliest possible point you can obtain a Legendary Pokémon is in Pokkén, which is technically a side game and therefore falls under your specifications. You can use Suicune as soon as you start the game.
If Pokkén doesn't count then I can hide my answer.