Well, I actually visited my first lodge 2 weeks after my initiation. Here, a EA can visit other lodges, when accompanied by a MM. Not all lodges do so, but most. We usually visit as FC, you actually have to visit as a FC, if you want to be raised. At least, many lodges hold it that way. My first visit was with a brother of my lodge to a lodge, he holds dual membership.
But personally, I would not vote for "as soon as I can". One should be versed in the own ways before visiting.