The primary reason is that this is not a pre-christian text, it is a re-telling of a pre-christian text that was written down, at the earliest, roughly a hundred years following the christianization of England around 700AD. As such, the speaker and audience most definitely were referring to God at the time the text was transcribed, even if the original characters were from a pre-christian culture.

Beowulf is actually a Christian text, and the God it refers to is the Christian one. While scholars debate to what extent the text contains elements of pre-Christian oral poems, the consensus is that the story we have was composed as a single piece by its Christian author. Precisely when it was written is up for debate (the manuscript in which it survives is from the early 11th century, but it's probably a copy of the original), but it's generally thought to be from around the ninth century, several centuries after England's conversion back to Christianity.

As for Latin and Greek translations, there's a few reasons you might see uppercase "God."

Sometimes the original text does just say "God." Take these two phrases in Aeschylus' Seven Against Thebes

εὖ τελεῖ θεός. "God will end it well"

l. 35

ποῖ δ᾽ ἔτι τέλος ἐπάγει θεός; "And to where does God yet lead us?"

l. 157

Both of these use the word θεός, "God." In the first passage, it's likely referring to Zeus, who has already been brought up. But to say "Zeus" would be to change the language beyond what is necessary for English sense. We see the same in Latin:

Ego nemini invideo, si quid deus dedit. "If God gives anything, I envy no one."

Petronius, Satyricon, 38

The same principle applies with deus. There's really no better translation than "God." It's capitalized because it's still referring to a particular entity and not just "a god," but that does not mean it's invoking the Christian God.

Other times it's done to clarify idioms. One often sees the Latin exclamation hercule roughly translated as "By Hercules."

Multo me turpior es tu hercule, "By Hercules, you are much more foul than me!"

Petronius, Satyricon, 10

The exclamation, though, is highly idiomatic. It's not terribly important that Hercules himself is referenced, just as most people who say "OMG!" don't actually have any deity they would call "my God." Translators will often replace this with "By God!" or "By Jove!" In either case, we are trashing a literal translation for one that preserves the meaning for modern earsl; "By God!" does sound much less antiquated than "By Jove!"

I've also seen translators supply "God" as an agent where sentences cannot be translated with typical English grammar. For instance:

Patrono meo ossa bene quiescant, "The bones of my patron rest [subjunctive mood] well."

Petronius, Satyricon, 39

English struggles with translating the subjunctive, especially on its own like this. I myself would translate this as "May the bones of my patron rest well." Other published translations have used "God rest the bones of my patron." I think that strays a bit too far, but it still works. Again, this is a rather idiomatic use of "God," and, as first discussed, wouldn't be too out of place in the text.

Lastly, it should be noted that Beowulf was composed after Christianity reached the region (most prominently during the 7th century), and though it depicts pagan figures, it's writer and audiences were influenced by, if not believers in, Christianity.