Growing up in the Cleveland area, many types of European sausages are everywhere. My wife introduced me to Thai and Chinese sausages which are much different but equally delicious. Only recently have I had English bangers and Irish white and black puddings. I can think of a few cultures that don’t seem to have any sausage like Eskimos and South Sea Islanders but then I am not familiar with their food at all.
Can I piggyback your thread and ask if all cultures have ravioli/pierogi/potstickers? (Are they considered dumplings?) Since we’re talking about Cleveland and European cultures and all, and we’re in high pierogi season.
Pretty much every culture whose cuisine I know anything about has some sort of stuffed dough; the only difference between them is what the stuffing is made from and how the dough is cooked - baked, steamed, boiled and/or fried.
A cursory Googling revealed nothing but:
I wonder if Japanese cuisine and the cuisines of the Indian subcontinent (especially of southern India) developed sausages before interactions with Europeans?
The aphorism here is: “Sausage is the logical outcome of efficient butchery.”
Just about every meat-eating culture has sausage. It serves two main purposes: it uses up meat and other food scraps, and preserves them.
Here’s an interesting Atlas Obscura article all about sausages:
Good write up. And one particularly memorable line:
“The fact that sausages resemble penises has been lost on precisely no one throughout the ages,…”
Does shish kebab qualify as sausage? If so, then yes, it exists in some form of Indian cuisine.
I suspect the answer is ‘no’ to both the original and follow up (sausages and filled pasta), but the no being predominately based on hunter gatherer societies in which grain would likely be rare. Even there sausages or the like may exist/have existed, especially ones such as blood sausage where they would have been prepared and cooked on the spot as a way to transport the blood and other highly perishable (and less portable) bits.
Of course, some might say that hunter gatherers past and present don’t have a ‘food culture’ as we would define it, and I would agree, it depends on your definitions. 
pemmican
And that’s why I made the exception for likely sausage, although the OP seemed to imply traditional European-style sausages in some form of casing, rather than pemmican which is a mix of dried meat, suet and possibly fruit/grains mixed together.
I’m not sure I’d even consider that a ‘loose’ meat sausage. More it’s own thing.
There are no native sausages (or dumplings, @ZipperJJ and @romansperson ) in Black South African cuisine.
Just to mention that one of my first jobs after leaving school was making sausages in a local butchers.
Natural casings (that I cleaned and prepared) made with quality back-fat and the offcuts of prime pork that were sliced off the roasting joints or gammons.
Minced up with herbs and spices they were top quality products from an excellent butchers who really knew how use every last bit of the animal.
One of my other jobs was making black pudding (but that was in a tray rather than in sausage format).
It was strangely satisfying to use my hands to remove the “strings” from the blood once it had cooled and mix in the fat, spices and barley.
What is done with butcher’s offal and trimmings in that cuisine? Is beef, for example, simply such an abundant staple food that it wasn’t considered necessary to figure out ways to use up the less appealing bits?
Or did said bits just get chopped up and put in stews and what-not, rather than being stuffed into casings made of intestine or pastry?
For tripe and the like, stews. Other offal gets eaten roasted (some offal, like liver and heart, are delicacies and would get roasted as the first edibles from a slaughter).
Beef was/is a rare celebration food, cattle is wealth and not for everyday slaughter. But I think “less appealing” is very much relative.
These are not cultures that are squeamish about eating anything - roasting sheep’s heads are a common roadside scene in the township markets:
I can understand no stuffed dumplings, but has no one every dropped some clumped up grain mixture into soups or stews?
Sure, it was specifically stuffed dumplings I was referencing.
Looked into this a bit, making sure there wasn’t more to shish kebab than what’s familiar in the U.S.
I don’t see a way that shish kebab qualifies as sausage.
This was my thinking. Back when butchery became a skill, in an effort to use up every part of the animal, people would gather-up all the little, left-over bits, look around for something to stuff them in - “hey, how about all this intestine?” Add little salt then gently cook, et voila, you have a stable and nutritious meal in a tight package that can last for a while and be taken along for whatever activity is next.
This part of the article makes sense:
One, to make use of every little piece of the meat, so nothing is wasted, and two, by using salt and smoking, it was a way to preserve it,” explains Gary Allen, author of Sausages: A Global History , pointing to the rise of coordinated hunting and the ability to pull down increasingly larger game as one of the conditions that led to the birth of sausages.
Yeah, definitely not for shish kebabs. That said, kofte/kefte kebabs (and similar items like adana kebabs or cevapi) might qualify as a type of skinless sausage (though I typically think of sausages as needing to be encased in something.)
Japanese Wikipedia has Japan’s sausage history starting in 1892.
Personally, I would be a bit skeptical since China (I believe) had sausage and the two countries had enough exposure to Chinese culture and cuisine that they certainly could have picked it up if they wanted.
That said, Japan banned the eating of land animals, starting about a thousand years ago. Previous to that, though, they could well have had sausage and - simply - forgotten the technique.