One day while discussing things with my friends, we came across the topic of trying to pronounce the sound [gh].
No such symbol actually exists in the IPA to my knowledge, but hypothetically it would be a velar stop that's both voiced and aspirated at the same time.
Can such a sound actually be made? According to Wikipedia they're opposites in terms of voice onset, which would make them mutually exclusive.
Definitely yes, only your phonetic notation is not very correct. Proto-Indo-European had such stops, Sanskrit and most Indian languages have them, too ([bʱ], [d̪ʱ], [gʱ], [dʒʱ], [ɖʱ]), the very name of India in Hindi, भारत [ˈbʱaːrət̪], has the [bʱ] sound, you can listen to the word here. Note, since the stops are voiced, so the aspiration is also voiced (which is reflected in the aspiration symbol ɦ), there is no problem in pronouncing them.
There is an article on Wikipedia about such consonants.
they're opposites in terms of voice onset, which would make them mutually exclusive.
As far as I know, that is true.
A sound that can be produced is a murmured plosive (they are sometimes called voiced aspirated). Whilst an aspirated consonant has the phonation type of a [h] a murmured consonant has the phonation of a [ɦ]. They are similar in that murmured voice let's more air escape than modal voice.
The answers given so far aren't quite accurate. True voiced aspirates are possible - they begin voiced and end voiceless, so there is no contradiction. An example (the example?) is the Kelabit language.
