No, not at all.
Here's what would be considered formal:
Поскольку Япония — страна достаточно от нас далекая, ...
It looks nothing like German, but there's cast-iron logic to the word order here. Just putting страна at the end when it's not the most informative word in the sentence is fairly relaxed.
*Достаточно далекая страна от нас sounds un-Russian unless you specifically want to stress от нас (as opposed to it being remote from someone else).
If there's anything formal here, it's the use of достаточно instead of the more generic довольно. Think "fairly remote" vs. "quite remote".