Pokemon Scarlet and Violet Sinnoh Starter: Where to get a free Sinnoh Starter Egg
Gift Pokemon are by no means a new feature for Pokemon, and indeed anyone playing Pokemon Scarlet and Violet: The Hidden Treasure of Area Zero are actually entitled to a Pokemon Egg containing a random Generation IV starter - a Chimchar, Turtwig or Piplup. You can even unlock it very early on in the expansion!
Where to find the free Sinnoh Starter
Shortly after you arrive in Kitakami, you can find your Homeroom Teacher from Paldea - Jacq - hanging around the eastern exit of the main town. By talking with him, he'll pull a whole charade to justify giving you a Pokemon egg. This egg will contain a random Sinnoh Starter. It will either be a Chimchar, Turtwig or Piplup - and you won't know which you got until the egg has been hatched..
Once you've got the egg in tow, simply explore around with it in your party long enough and it'll hatch - revealing which Pokemon you've been gifted. One small thing to note, is that despite being a Pokemon that you can technically catch in Kitakami, none of the Sinnoh Starters are part of the new Kitakami Pokedex, and won't apply towards any Pokedex completion rewards. Have fun with the rest of your Kitakami vacation!