This is a very good question about how Greek uses the definite article differently from English. In summary: "the Word was God" is best. Here's a short explanation as to why:
1. Greek uses "the" much more often than English
John 1:1 in Greek from Bible Hub: (every definite article in bold italics)
Ἐν ἀρχῇ ἦν ὁ Λόγος, καὶ ὁ Λόγος ἦν πρὸς τὸν Θεόν, καὶ Θεὸς ἦν ὁ Λόγος.
Greek uses the definite article (the) much more frequently than English because Greek nouns have case:
There are five CASES in Greek, the nominative, genitive, dative, accusative, and vocative.
...The case even includes the definite article. That would be like "a" or "the" in English having a different spelling if it was for an object, direct object, subject, possessive, etc. This is part of why so many Greek words also have "the".
Also, there is no indefinite article in Greek (a/an). In Greek, it's all the same.
2. Greek uses "the" with names
If we were consistent in translating "the God" from John 1, then Mark 10:51-52 and John 6:1 would say "the Jesus":
...There are countless other examples throughout the New Testament with countless other names. Names don't always get the article, but they often do; English never does.
3. Greek doesn't always use "the" with "God"
Notice that in John 1:1 "τὸν Θεόν, καὶ Θεὸς" the second time "God" appears, it is Nominative (subject) and doesn't have an article. This happens again in v6 in the Genitive (origin) "παρὰ Θεοῦ" (lit. 'from God').
If anything, that is a strong argument for not translating "the God" anywhere else, because Θεὸς is not so dependent on use with an article.