Many players like to reset their game until their starter Pokémon has certain traits, like being shiny. However, in Pokémon Scarlet and Violet (SV) starters are shiny-locked, meaning the Sprigatito, Fuecoco, or Quaxly you pick at the beginning of the game cannot be shiny no matter how many times you reset — so no, you can’t hunt for shinies right at the start of the game. But there is still one option.
Breeding Is the Only Way to Hunt for Shiny Starters at the Start of Pokémon Scarlet and Violet (SV)
The only method to get a shiny early in the game in Pokémon Scarlet and Violet is to breed your starter, which is only possible if you have a female starter or find a Ditto. Even if you breed your starter, the odds are extremely low, at the usual 1 in 4096 rate from other recent games.
The only way to speed up the hunt for shiny Pokémon, starters or otherwise, in the early game is if you breed Pokémon whose original trainers had different language settings chosen at the beginning of the game. For example, a Ditto traded from a Japanese-language game and your own English-language starter would give improved odds. In this case, your odds will be 1 in 682.6.
You might be better off breeding a shiny starter later on in Scarlet and Violet, once you unlock the Shiny Charm, but if you want a shiny starter early on, those are your options. Having to wait a bit for a shiny Sprigatito, Fuecoco, and/or Quaxly will make it all the sweeter in the end.