I renovated a van into a camper van so I have a good amount of experience in this area. During my reno (and most other people too) you rip everything out so it's basically a tin can. Let me tell you, it's loud! There is a company out there called Killmat, but it tends to be hard to find and overpriced. Another company Siless is the same thing and always available. I can't say enough about it. They are pre cut squares, you just peal the back and stick it on. You can cut it before or after with a utility knife for exact fits, it's easy. They also come in different thickness's for more sound deadening. Then just throw your carpet on top of that. I'm fairly certain I'm going to do it this fall after a few other projects.
https://www.amazon.com/Siless-mil-sqft-Sound-Deadening/dp/B0BKP6JDWD/?tag=wranglerorg-20
https://www.amazon.com/Siless-mil-sqft-Sound-Deadening/dp/B0BKP6JDWD/?tag=wranglerorg-20
