In terms of ranking, competition, is it idiomatic to say “won/took THE first place“? I have always used and heard it without the definite article.
There's a clear-cut idiomatic divide between including the article or not, depending on whether the verb is to win or to take. As this NGram chart shows, it was far more common to include it until about a century ago with took the first place. But per this chart, the usage won first place wasn't well-established until about then, so it gained traction using the newly-favoured "article-less" form.
Having said that, both versions are at the very least "acceptable" with a broad range of verbs (including receive, share, obtain, gain, etc.) and of possible things won (second prize, [the] gold [medal], etc.).
But on average, if you find similar numbers of matches for versions with and without the article, the latter will almost certainly be predominantly the more recent instances, so you should copy them.