This not being a coincidence is the Altaic Family Hypothesis, which posits that Turkic, Mongolic and often also Japonic and/or Korean languages form a superfamily, sharing a common ancestor. The hypothesis is mostly discredited by present-day linguistics.
Is that the only explanation though? Could proximity explain things? It is my private theory that German and Polish having had so much geographic overlap explains some common features, despite being from different families.
I don't know to what extent this has happened with German and Polish. They are, of course, (somewhat distant) cousins in any case, both being Indo-European languages.
But it is often the case that geographically close languages influence each other -- the term in linguistics is "sprachbund". If one is entirely honest, a lot of languages have taken vocabulary or grammatical features from one or more languages from other language families, rendering the entire idea of a language "family" (the word is here evoked to imply a pure genetic lineage) kind of suspect to begin with. But it still is how linguistics is commonly done today.
The basis for my very non-scientific observation is that I am a native Dutch speaker, who's conversational in German and has a Polish partner. German fits quite well in between Polish and Dutch in terms of features: Dutch has few, Polish has nearly all, and German has quite a few more than Dutch ;) Similarities between Dutch and German are more easily understood since they've a recent ancestor, but for Polish and German we must go back much further. Yet, my untrained eyes see a sort of continuity that seems to cross the language-family barrier, which could make sense because of that shared geography of German and Polish. I know that Poles have a history of fervent conversationalism that favors (grammatic) complexity, so perhaps it's a hobby that spilled over to German-speakers. Or vice versa (I know less of German cultural history).
indeed; but still incredible that it retained so many characteristics over time and at such great distance from origin! I had been very fascinated with this.