I think hacks can do that. I'm not sure if anything else can make that happen.
event Pokemon often come at random and/or impossible levels, such as a lv1 shiny golbat. (random idea for an event since my fried asked me if my shiny golbat was an event lv1 for some reason)
loving the gif by the way
Other than hacking, there are a few ways that you can get an evolution of a Pokemon that normally evolves by level up. One of these ways is breeding. If, for example, you breed an Azumarill or Marill that isn't holding a Sea Incense, then the Pokemon that comes out of the egg will be a Marill on level one. As Azurill evolves through levelling up with enough happiness, Marill is one of the few Pokemon that can be evolved on level one. The second and final (As far as I know.) method of getting the evolved form of a Pokemon that evolves by level up on level one is events. I'm not sure if it has ever happened, but I'm almost certain that it is possible, as Pokemon have been distributed at level one before.