While the particle šĕ (שֶׁ) is predominantly found in "later" books -- especially Ecclesiastes and Song of Songs -- it is not an inevitable sign of lateness in the language.
There are also examples in early books, one of the most striking occuring in the "old" poem, the Song of Deborah, in Judges 5:7 -
The peasantry ceased, they ceased in Israel,
Until I [עַ֤ד שַׁקַּ֙מְתִּי֙], Deborah, arose,
Until I arose, a mother in Israel.
The standard work on this is Gotthelf Bergsträsser, "Das hebräische Präfix שׁ," Zeitschrift für die alttestamentliche Wissenschaft 29 (1909): 40-56; Paul Joüon's grammar (§ 38) also asserts that it must have "existed at all times in the vernacular".
So far as I'm aware, Bergsträsser is still followed in the view that the particle is related to Akkadian ša. For a very full discussion of this phenomenon, see Robert Holmstedt, "Historical Linguistics and Biblical Hebrew", in Diachrony in Biblical Hebrew, ed. by C.L. Miller-Naudé and Z. Zevit (Eisenbrauns, 2012) with the relevant discussion on pp. 113-119.
So, no -- the use of this particle is not necessarily a pointer to lateness in biblical Hebrew usage.