Doest it mean "from"? The writer wants to conclude that human brain is asymmetrical from the outset of existence:
The part of the brain responsible for control and movement is located in the left hemisphere, and the findings above suggest that the human brain was already asymmetrical not long after 3 million years ago.
The phrase
not long after
is a relative period of time after, since, or starting from a reference event.
How much time is dependent on context:
He went outside and not long after it started to rain
would usually be measured in minutes.
Not long after Tyrannosaurous Rex disappeared Stegosauruses roamed the earth
would be measured in millions of years, otherwise known as geologic time.
In your example
the human brain was already asymmetrical in its structure and function not long after 2 million years ago
would be measured in tens of thousands of years and put the starting time more recent than 2 million years ago, otherwise known as evolutionary time since generations of a species need to occur for change to happen
NOTE: There seems to be anecdotal evidence that humans are not the only mammals with a preference for handedness here, here, and here. Gives real meaning to the term southpaw.
