It is not uncommon, at first, to consider producing your own hydrogen. This has been done successfully by one individual and his balloon circumnavigated the world once. In general the effort is rather big and is just generally a poor idea. If you intend to produce hydrogen with wet chemistry, make sure you know enough about chemistry and the kinetics of a reaction to control what you are doing. If you follow some of the Youtube videos where wads of aluminum foil or soda cans are used, realize that you have started a reaction over which you have no control. If you cannot stop a chemical reaction, you should not start it. If you use some of the gas generators being demonstrated on Youtube, make sure you know what you are buying or building. Some of them produce an explosive mixture of hydrogen and oxygen and things will not go well.
Producing hydrogen can be done with electrochemistry or chemical reaction. Either way, the gas you produce will be saturated with water and will need to be dried for the balloons to function properly. Remember that the balloons will be at temperatures of -50F or so and all the water vapor will be ice. Not a good thing to have in your balloon.
If you choose to produce the gas with electricity, do the math and realize that you are going to need about 5 moles of gas to function and each mole will require two Faraday Constant of electrons to product. That is 96485.3 coulombs each. A coulomb is the number of electrons in one ampere in one second. This is a pretty hefty power supply and will take a lot of time. It is, however, something you have total control over. You can probably use a low cost electrode and pvc to do these things. Seems like a lot of work for something you can buy at the local welding shop.
To just ballpark the prolem, an SBS-13 balloon will require about 10 grams of hydrogen. That is 5 moles. Each mole will require 2 Faraday Constants of charge so 10 Faraday Constants. Each Faraday constant is roughly 95,000 coulombs so 475,000 coulombs. A coulomb is the charge carried by one ampere in one second. A 100 amp supply would require 4,750 seconds or roughly 1.3 days. You will not have 100% efficiency so it could easily be twice that. This is not a trivial task.
You can choose to produce the gas with a chemical reaction. There are a variety of videos doing such a thing on Youtube. I see things like a wad of aluminum foil and muriatic acid. They toss the aluminum foil in the acid and step back. Once the reaction begins to go, it increases rapidly. That is a good reason to step back. Notice that the temperature and surface area involved in the chemical reaction is not controlled. There is a huge surface area in a wad of aluminum foil and when the reaction begins, the temperature is rising quickly. The high surface and temperature make this dangerous. I believe the Youtuber did get garbage bags to lift off. In reality you will need to also dry the gas and carefully measure and control the lift of the balloon. Things will not go well. Don’t do that. Soda cans will be problematic because they are coated and very thin. They won’t work well either.
If you insist on producing hydrogen with chemistry. Consider the aluminum water reaction. It requires a small amount of sodium hydroxide to keep the surface active as aluminum forms an oxide coat which protects it from the outside world. If you use thick pieces of aluminum, like aluminum angle from a hardware store, the surface area will be stable. If you have a heating mantle and the glassware to do this and if you have a condenser to provide reflux, you can produce hydrogen with reasonable possibility of control. And don’t forget you now need a cooling water supply for the condenser, The gas will still need to be dried for the balloon. You can see the problems here. A heating mantle with temperature control, glassware for the reaction vessel, a reflux condenser to contain the water evaporated by the heat of the reaction, a water supply, a drying column to finish the water removal, This is such a poor idea compared to buying a cylinder you should not do it.