Translation:I want him to arrive as early as possible.
The expression "at the earliest" bothers me a bit here. It seems to me that the expression has two possible meanings in English, but in neither case does it stand on its own.
You can say "at six at the earliest" meaning not before six, or "at the earliest possible moment." Which is what I guess the Italian sentence means, but in neither case can you leave out the time reference and still have the expression make sense.