This U.K. promotional video for a soundproofing company shows samples of some of their soundproofing products, which are similar to those in the USA. They also talk about some of their methodologies, though not in detail. But just looking at the products might give you some ideas. Note the example of the sheds near the end. It would have been nice to know what they used in the 60% soundproofed shed (it looked like mass-loaded vinyl and a Homasote-like product), as well as the 100% !!
It's not too late to insulate. A few years ago, most American homes had no insulation in them. When a homeowner did insulate, it was usually with fiberglass batts. Then along came some better products. One of them is blow-in cellulose insulation. Does it work? I can attest to this: YES. I've used it in walls and ceilings, and it works quite well for airborne noise. If you live in an uninsulated home and you hear your neighbors voices coming through your walls or ceilings, cellulose will dampen that noise or mute it entirely. It doesn't work for all types of noise. But it doesn't eradicate impact noise. You might still hear the sounds of someone walking across a bare hardwood floor with their shoes on, for example, or hear wall-mounted cabinets opening and closing. There are other solutions for that, and by combining different solutions you can control most structural noise and create more privacy. Low cost Blow-in insulation is inexpensive. You can hire a