I can actually answer this one! In my graduate level women's history class we studied the case of Thomasine/Thomas Hall in one of Mary Beth Norton's primary source collections.
Thomasine was born in London and identified herself as a girl. However, when she matured she changed her name to Thomas, started dressing as a man, and even joined the army. In 1627 he settled Virginia. His gender identity was almost immediately questioned. One night while he was asleep some neighbors snuck into his room check what was under the covers. During one incident he was accosted in the middle of the street by influential members of town and forced to strip naked. It became such an issue that the local magistrate had to order Thomas to identify his true gender. The case of Thomasine Hall's gender identity even made it as far as the Virginia Supreme Court. The case is still on record.
If you're having trouble understanding why the colonists spent so much time and energy figuring out Thomas' gender, then it's helpful to keep in mind that colonial America operated by a very strict social hierarchy. If you met somebody on the street that you didn't know them, then their gender and clothes would largely determine how you interact with that person and how they relate to you in the social hierarchy. Because there was the question of Thomas' gender people didn't know how to classify him and where he fit in the hierarchy, which was a threat to the system itself.
I can't seem to find the same primary source I used, which is unfortunate because there are a lot of hilarious quotes in there from colonists trying to understand what a hermaphrodite is. Here is a link to a NYT book review of Norton's book that covers the case and also a link to a JSTOR article that covers the case in more detail.
New York Times http://www.nytimes.com/1996/04/28/books/daughters-of-the-revolution.html
Known likely transsex people throughout history include:
It's hard to tell who was actually transsex and who was just trying to escape the rigidly enforced gender roles of the time, with other cultures' specific third-gender roles further complicating things, but it's a fair bet that at least some of these people were genuinely transsex.
At any point, the condition most certainly existed long before the means to fix the body of those afflicted by it.
Edit: more detail required? OK, let's see what I can find:
Here's a excerpt from The Crimes of Elagabalus: The Life and Legacy of Rome's Decadent Boy Emperor:
After [Dio] has mentioned that Elagabalus circumcised himself... he remarks that the emperor "had planned, indeed, to cut off his genitals altogether", adding, "but that desire was prompted solely by his effeminacy." In two inserted passages, it is stated that the young monarch wanted a vagina implanted in his body by means of an incision... It seems safe to assume he is the original author of this anecdote as well.
Chevalier d'Eon's memoirs, La Vie Militaire, politique, et privée de Mademoiselle d'Éon are ghostwritten and likely embellished, but should contain insights into d'Eon's motivation. Alas, I don't speak French. At any rate, this individual cross dressed persistently enough for the London Stock Exchange to make a betting pool regarding their sex.
James Barry was a card. Not particularly personable, but he improved the lives of many people. It's difficult to say if he was a transsex man, or a woman who had to adopt a male guise in order to pursue a career before organised feminism. Similarly, Charley Parkhurst was a particularly good stagecoach driver whose male identity could have been either genuine or merely practical. The same goes for the soldier Albert Cashier, although you might think that had he not been sincere in his male identity, he perhaps might have risked confiding in his employer when he worked as a farmhand, which he doesn't appear to have done.
We'wha was a Native American. Just as different cultures divide the continuous spectrum of colours up into different identifiable colours with different names -- to oversimplify, some might have red, green, and blue, and others yellow and turquoise, with much debate amongst people from both cultures about whether a particular colour constitutes being blue or turquoise -- so do they divide genders up at different points with different names, with people having to find the closest fit. As such, it's difficult to say how many of the people deemed to be male bodied and at least significantly female spirited would of their own volition identify as female and opt to fix their body to reflect that if given the option, or how many counterparts there might be in the opposite direction had that been an option.
Jennie June wrote two autobiographies which should provide some insight to her motivation, albeit in the less enlightened vocabulary of the time regarding such matters.
Lili Elbe was likely intersex, and passed for a cissexual woman better than a cissexual man even before she changed sex. She managed to do the latter thanks to various doctors, including Magnus Hirschfeld, who pioneered helping transsex and gay people in Germany until his work was destroyed by Nazis.
Alan Hart likewise changed sex, although in both cases this was before widespread knowledge about such possibilities, making it very likely that they would have had to either painstakingly seek out such services on the offchance they existed, or happen to be amongst the lucky few who stumbled onto them while their contemporaries suffered in silence.
Victor Barker and Billy Tipton are two more examples of individuals who persistently cross dressed for significant portions of their lives, again something people would be unlikely to do were those not their true identities, given the deep melancholy that accompanies living a lie.