Is there evidence that Isaiah 53 was viewed as a Messianic prophecy within Judaism, or is it an exclusively Christian interpretation? The modern Jewish interpretation of the so-called suffering servant song of Isaiah 52:13-53:12 is that it is a prophecy referring to the nation of Israel, not the Messiah.  As such, it is sometimes suggested that Christians invented the idea that this is a Messianic prophecy.

What evidence is there that (at least some) Jews saw the passage as having Messianic implications?  Do such interpretation predates the advent of Christianity?  When did the nation of Israel interpretation become common?
The existing answer provides a learned and fascinating discussion for tracing the interpretative history of Isaiah 52:13-53:12 (often conveniently abbreviated to "Isaiah 53", the so-called "Fourth Servant Song") from roughly the 1st C. CE. Thus, the conclusion...


  We can ... be confident that first century converts to Christianity did not invent the idea that Isaiah 53 has Messianic tones.


...can be placed on a stronger footing if we also modify this claim:


  [w]e have no data at all on interpretations for the first 500+ years after the passage was written.


There are three, at least, sources of evidence for this period: (1) the Hebrew Bible itself; (2) the Septuagint (Greek translation of the Hebrew Bible from the 3rd-2nd C. BCE); and (3) the Dead Sea Scrolls.

(1) Martin Hengel (towering scholar of late Second Temple Period and early Christianity) drew attention to later texts in the Hebrew Bible that, he argued, showed the influence of Isaiah 53 and pointed in a messianic direction.1 He argued for lines of connection and relationship between Isaiah 53 and (a) Zechariah 12:9-13:1 and 13:7-9, and 12:10 in particular; and (b) the book of Daniel 11:33-35 and 12:2-3. This is explored and stated with some care, especially the Zechariah connection, but for Daniel, Hengel points to the study of H.L. Ginsberg arguing that it is "the oldest interpretation of the suffering servant" (pp. 91-92).2

(2) The Septuagint actually doesn't offer much in this passage, but it does need to be mentioned. Its overall "messianism" has been much discussed,3 so it might be surprising (in light of later history) that any messianic overtones there might be in Isaiah 53 are subdued in the pre-Christian Greek translation.4

(3) The Dead Sea Scrolls give us more, especially in the "Great Isaiah Scroll", 1QIsaa. Among other considerations, Hengel draws attention to two variations in particular that point to a "messianic" understanding for this "Servant Song":1


52:14 includes an obscure hapax legomena מִשְׁחַת that appears in 1QIsaa as משׁחתי which pointed would be מְשַׁחְתִּי məšaḥtî, "I anointed". This, in conjunction with the added definite article on ʾadam, results in a text which Hengel translates: "I have anointed his appearance beyond that of any (other) man, and his form beyond that of the sons of humanity [the human]". This has other textual overtones bringing the passage into an explicit connection with "anointing".


53:10 in the MT includes what is widely regarded as a textual corruption, הֶחֱלִי "he made him sick". Here, the Isaiah Scroll has ויחללהו, "he pierced him" (and 1QIsab has a gap). Hengel notes and discusses the connections back to Isa 53:5 where "pierced" is also used, and the further connection to Zechariah 12:10 (see also above).




In summary, the OP's "self-learner" conclusion looks to be sound after all: there are indications that a pre-Christian understanding of Isaiah 53 included some sense of its association with an (or "the") "anointed one", i.e., mashiach. It is admittedly not pronounced, but neither is it absent. Further exploraton of this body of evidence would further reinforce this impression. (Anyone minded to follow-up the secondary literature cited will find more than enough to substantiate this claim.)

Finally, we must bear in mind Hengel's own caveat (p. 103):5


  [W]e must remember that in the second century B.C.E., we do not yet possess any fixed Jewish doctrine of the Messiah&mdash;there basically never was one&mdash;but must rather deal with various ideas of anointing and the Anointed One.




Notes


M. Hengel with D. Bailey, "The Effective History of Isaiah 53 in the PreChristian Period", in The Suffering Servant: Isaiah 53 in Jewish and Christian Sources, ed. by Bernd Janowski &amp; Peter Stuhlmacher (Eerdmans, 2004), pp. 75-146. This chapter should be read by anyone interested in the subject; other chapters in this volume also have relevance for this discussion.
H. L. Ginsberg, "The Oldest Interpretation of the Suffering Servant," Vetus Testamentum 3 (1953): 400-404.
See e.g. this review of R.F De Sousa, Eschatology and Messianism in LXX Isaiah 1–12 (2010) and the literature cited there. Also, substantially and recently, Abi T. Ngunga, Messianism in the Old Greek of Isaiah: An Intertextual Analysis (Vandenhoeck &amp; Ruprecht, 2012).
For details, see David A. Sapp, “The LXX, 1QIsa, and MT Versions of Isaiah 53 and the Christian doctrine of atonement,” in Jesus and the Suffering Servant: Isaiah 53 and Christian Origins, ed. by William H. Bellinger Jr. and  William R. Farmer (Trinity Press, 1998), pp. 170-192.
This with reference to the Great Isaiah Scroll in particular, but it is true of all the evidence for a pre-Christian understanding of the "messiah".