At most grocers, you can purchase carbonated water that is only CO2 and water. I use it t make homemade cream soda.
I once took a sliver of dry ice, and put into a two liter, clean, plastic water bottle, along with strawberry Kool-Aid and water. I screwed the cap on tight. I had to release pressure twice to keep the plastic bottle from exploding. Even then, the bottle was expanded by the time the dry ice was gone. It made some very fizzy strawberry soda. My youngest daughter was amazed that I could make soda-pop at home. I had experience on my side though.
After high school, and just before going into the U.S. Navy, I worked at a soda-pop bottling plant. We made Verner's, RC Cola, Upper-Ten; Frosty Root Beer,, and Both Nesbits, and Nehi fruit flavored sodas (orange, strawberry, grape).. Th process was simple. 2 foot square blocks were placed by hand into10 foot steel pressure tanks, the lids were screwed on with cheater bars to get them sealed. 200 gallons, 200 lbs. cane sugar, and 1 gallon of soda concentrate were poured into stirring tanks, and let mix for thirty minutes. Bottles were washed and loaded into the bottling machine, and the machine was set to add an amount of the pop syrup to each bottle, according to the recipe for the specific pop, and the carbonated water filled the bottles. They were capped, and one person was in charge of inverting the bottles twice, to mix the syrup with the carbonated water, and the bottles placed into crates for distribution. Good people worked there. They'd all grown up on the tough side of the tracks, and were probably looked down upon by our town's hoity-toity types. But they were really great guys. I trusted them to be honest, hard working, and good friends.
I must have looked a sight, weighing in at about 95lbs., soaking wet, and carrying 200 lb. sacks of sugar, and driving a fork lift carrying pallets of bottles ten foot high. But I did all the same work as the other workers, which included the foreman, one other recent high school grad, one truckdriver, and one assistant floor manager. The foreman, years later, told me that he hadn't thought I'd have lasted a week, due to my small size, and that I really surprised him by carrying my load, and then some. We all got along great, and occasionally got a little, um. inebriated after work, on site. They liked peppermint schnapps. Me, I hate mints, and detest the flavor of alcohol, and so drank the root beer. I got razzed a little for that, but not badly. I also got to know the foreman's family, and shared a meal or three with him, his wife, and kids. I've always been great with kids.
Good memories. Sorry to go so far off track. But like I said, good memories.
Oh, and about ginger ale, and ginger beer, The original root, and birch beers got their carbonation from yeast fermenting in the brew, just like more familiar ales, and beers.. It wouldn't' surprise me if ginger beer wasn't initially made through yeast fermentation as well.
Oh, I looked up ginger ale history, and found this -
https://en.wikipedia.org/wiki/Ginger_ale
Seeeeya; Chief Longwind of the North