Depends on how much competing interest is out there.
A Petri dish might dream of taking over North America, but the humans might have other plans (for instance, the autoclave across the room).
Maybe they'd reason that North America is entirely lifeless, since nobody has yet tried to communicate the secrets of the Universe to them in a (bacterially) intelligible language.
Honestly the Petri dish has better chances. The bacteria that inhabit one already have the demonstrated ability to persistently survive outside of it.
>the galaxy, or at least the local group
The local group is bigger than the galaxy.