While I don't believe you're going to really find an answer to this question (or else, you may just find that the answer is "no"), here's an example that may give you something to think about:

Aeschylus, the Greek tragedian, wrote Persians, a play about the Greco-Persian Wars -- a series of wars in which the Persian Empire attempted to subjugate the Greek city-states. In it, the mother of the Persian king, Xerxes, has a prophetic dream:

Two women stand before her, one dressed in Asiatic finery, the other in the more simple Greek garb. "sisters too they seem'd, / Though distant each from each they chanced to dwell, / In Greece the one, on the barbaric coast / The other." Dissension soon rises between the two, and the Persian king intervenes. He yokes them to his car, harnessing their necks.

"The one, / Exulting in her rich array, with pride / Arching her stately neck, obey'd the reins; / The other with indignant fury spurn'd / The car, and dash'd it piecemeal, rent the reins, / And tore the yoke asunder; down my son / Fell from the seat."

The two women in the dream are understood to represent the lands of Greece and Asia, both of which the Persian king was attempting to conquer. Richly dressed "Asia" takes the subjugation in stride, even taking pride in her place beneath the yoke. The other, dressed in Doric garb, can not be satisfied to live under the yoke of another, and bucks the king.

According to Edward Said, "Aeschylus represents Asia, makes her speak in the person of the aged Persian queen." He identifies Aeschylus' Persians as the earliest example of "a highly artificial enactment of what a non-Oriental has made into a symbol for the whole Orient."

Aeschylus repeatedly refers to the the realm of the Persians as "all of Asia" (for instance, lines 56-57). Not that the land of Persia is all of Asia, but that Persia controls all of Asia, drawing from "all of Asia" for its armies' strength.

In the book, Brill’s Companion to Greek and Latin Epyllion and Its Reception, the image is taken further: "Asia and Europe are personified as two women whom Atossa's son, Xerxes, wants to subjugate. In analogy to this, Europa dreams of two women fighting for her; one of the two is called Asia, whereas the opposite continent has to be left unnamed, of course."

Here, the author is referencing the Greek myth of Europa, in which the goddess Europa dreams of two continents fighting over her, both of which have taken the form of a woman. See: ancient Greek poet, Moschus, in his Europa

So, we don't have a symbol of Asia here, exactly, but a personification of Asia, in the form of a woman. This image, and the traits associated with the image Aeschylus employed, would be very influential on the perception of Asia within Europe.

Edit: I had a quick idea. How does the Chinese written language represent "Asia" or the general continent on which their nation resides? I am in no way an expert on this, but my understanding is that the Chinese script is based on pictures (the more recent in history, the more abstract the script became). And so, my reasoning goes, if they have a name for the land as a whole -- and not just for "china" or the "barbarian lands"-equivalent -- then perhaps this could be seen as a rudimentary form of symbolization for the continent.

What do you mean by this?