NixOS does not fit into this, but Nix the package manager could.
> Nix is a purely functional package manager. This means that it treats packages like values in purely functional programming languages such as Haskell — they are built by functions that don’t have side-effects, and they never change after they have been built. Nix stores packages in the Nix store, usually the directory /nix/store, where each package has its own unique subdirectory such as
> /nix/store/b6gvzjyb2pg0kjfwrjmg1vfhh54ad73z-firefox-33.1/
> where b6gvzjyb2pg0… is a unique identifier for the package that captures all its dependencies (it’s a cryptographic hash of the package’s build dependency graph). This enables many powerful features.
https://nixos.org/guides/how-nix-works.html
Git LFS / Git Annex might be able to suit your needs, but they're essentially "just" Git with some modifications to make large files easy to work with.
One of the "powerful features" of Nix mentioned above is reproducible builds, which sounds like what you're looking for.