Yes. "C'est" would be used with something specific other than the weather or ambiance, and it can mean gloomy, somber, or shadowy (figuratively).
C'est un homme au visage sombre. = He's a man with a dark countenance (gloomy face).
C'est une sombre histoire de trahison et de meurtre. = It is a grim story of betrayal and murder.
Here are some links to Larousse and Word Reference for additional uses of "sombre"
My response of "It's dark out" was not accepted. Since the sentence starts with "il fait", I believe that means it's referring to weather, rather than a person or thing. So the meaning "It is dark" should be acceptable because it's generic and might refer to weather or some other object, but I think "It's dark out" should also be accepted.
"Il fait sombre/noir" does refer to the lack of light rather than an object as you surmised. It's dark! However, I'm not really sure if "out" should be accepted or not since words that do mean "out" and "outside" (dehors/à l'extérieur) are not a part of this sentence...and they could have grammatically fit at the end of this sentence.
The "il fait + ..." is idiomatic in French.
Il fait beau = it's a nice day.
Il fait du soleil = it's sunny.
Il fait jour = it's daytime/it's daylight.
Il fait mauvais = it's bad weather.
Thanks for your response! It seems to me that if "Il fait du soleil" means "It's sunny" and it's never truly sunny inside, then similarly "il fait sombre" is likely to mean "it's dark outside". But this wouldn't be the first time DuoLingo failed to agree with me on a nuanced difference. Anyway, your response was helpful. Thanks again.
The impersonal "il fait" is used to express weather in French. Here it doesn't mean "he makes/does", but rather the "weather is/it is."
Whenever you see "il fait" followed by beau, mauvaise, sombre, froid, chaud... you can be sure it is a reference to the weather.
Just like English verbs take on multiple roles, so too do French ones!
"Il fait" can mean "it is" or "the weather is". In this case, "the weather is" is a clearer meaning and should be accepted.