It may be impossible.
All successful real-world language decipherments—Linear B, Egyptian, Hittite—have involved connections with other known languages. Linear B (Mycenaean) is closely related to Classical Greek, for example; Egyptian is related to Coptic and a bit more distantly to Hebrew and Arabic; Hittite is a distant relative to the whole Indo-European family.
Even if you only look at the writing system, figuring out Linear B involved connecting known place names like "Knossos" with words that were more common in inscriptions at Knossos than elsewhere. Ventris's biggest breakthrough came when he hypothesized that Kober's
??-C₄V₂-C₂V₂ might be k-no-so, which gave tentative values for C₂, C₄, and V₂, and extrapolated from there.
With an alien language, we have no idea what names they used for places. We don't have any loanwords or names transcribed in other languages to compare against. We don't know if they use anything resembling phonetics to communicate—or if their language is even fundamentally based on recursion like ours is.
Maybe humans and Thulians have never made contact before, but the Borean language is known, and an ancient Borean imperial decree—translated into Thulian—is found in the excavations.
Maybe Thulian and Borean are part of a language family—that hints to the linguists that Thulian might use a stack-based syntax (or whatever other weirdly inhuman feature you like) just like Borean does.
Maybe there's some old Thulian technology stored in Area 51, taken from a crashed spaceship; it contains records of an early Thulian attempt to figure out human languages (maybe even a rudimentary grammar of English written in Thulian).
Maybe they can find a live Thulian, or, failing that, an artificial intelligence of some sort, which can give them real-time feedback—a native speaker is orders of magnitude more useful than any inscriptions can ever be.
Maybe Thulian is related to some obscure Earth language(!). There used to be contact between Earth and Thule, which stopped millennia ago, and Thulian shares a distant ancestor of Etruscan/Sumerian/Pirahã/your favorite real-world language isolate. (Though be prepared for a lot of strong linguistic opinions if you decide to weigh in on the Pirahã controversy!)
Maybe universal grammar (in whatever form you like) is universal even across planets, and Thulian still has recognizable levels of phonology, morphology, and syntax.
None of these on their own would make decipherment easy—but the more you add, the easier it gets. At some point, it becomes possible, and that's what matters for a story.