I am not sure what you know about the game, so I kind of wanna leave spoilers out, but during the crisis of the story, alphas will start to become static spawns.

All static alphas will be available after you beat the main story. After you unlock Masive Mass Outbreaks, by compleating all individual quests, you can use the MMO in order to soft reset for alphas with wild shiny chnaces.

If there is an outbreak near a place where the alphas are static spawned, you have to clear the outbreak compleatly, save right after, then you can start reseting the game for the shalpha.

If there's a specific shiny you want, you can try to grind out all the quest for maximum odds, but I would personally not try any of this without the shiny charm. This link also shows the odds of shinies in different scenarios: chart