僕はどうにかそこに着くのに間に合った。

English Translation

I somehow managed to get there in time.

Would 何とか also work?

@ericaw
なんとか is actually better than the original sentence.
そこに is very redundant and the overall word order is unnatural. I would propose:

僕はなんとか時間内に到着できた。(pron. じかんないにとうちゃくできた)

どうにか is often followed by する/して or こうにか. And

僕はどうにかして○○を間に合わせた。(Note: not 間に合った but 間に合わせた as a transitive verb)

is the right collocation.

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