No, prehistoric Neanderthals did not make any significant tools and art or develop any complex language.
They therefore did not have a culture that we know of.
Even though they did have brains as large as ours and lived concurrently with Homo sapiens at a time when humans were making tools, painting caves, and traveling the sea, the Neanderthals were apparently a pretty dim cousin; hence the derogatory term.
There’s no known art from them, and no evidence of technological advancement, leaving a strong suspicion that these strong silent types were literally that.
They may have never even developed a language.
The Neanderthals died out about 35,000 years ago. Homo sapiens aren’t due to go extinct for at least another decade or two.