Question

Is there a way to get a specific Pokémon in an outbreak in legends Arceus?

Comments

It only affects Pokémon you’ve caught, so if you really wanted a certain Pokémon, you could go through the game without catching anything unnecessary

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that's a problem because I have finished the pokedex.

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No; it's RNG based, however the new feature, Massive Mass Outbreaks can hold multiple Pokémon in outbreaks.
From my playing the game, the 3 starters can only appear in space time distortions and these outbreaks
Cyndaquil: Crimson Mirelands
Rowlet: Coronet Highlands
Oshawott: Alabaster Icelands
Pokemon that are hard to find in the wild, like Cherubi, can be found in the Obsidian Fieldlands in outbreaks, however in my playing, I have found one Cherubi outbreak.  
With all my rambling over, there isn't a way that I know of to make certain Pokémon outbreak.

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> there isn't a way that I know of to make certain Pokémon outbreak.

There might be a way of doing the mentioned thing that you aren't aware of.

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There isn't. It's random.

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@Spex That comment was initially an answer and lacked a proper source so I pointed out that statement in their answer and said they should comment instead if they're not sure. The answer got turned to a comment so I removed the latter part from my comment and hence the misunderstanding.

Answer 1

According to Screenrant:

Unfortunately, Mass Outbreaks are also rolled at random.

Outbreaks occur only with Pokémon you have caught before. They don't work with Legendary or Mythical Pokémon.
If the desired outbreak doesn't appear on your map, you can leave Jubilife Village, then go back to the village and check your map again. This process takes a long time, however.
Another way is by investigating a Massive Mass Outbreak- seeing as this is multiple Outbreaks at once, you may have a better chance of finding the Pokémon you want.