The Cache System/Cachix is not working

No repository file, test, or entry point is identified. Start by reproducing the fresh Ubuntu installation and reviewing the displayed Nix and Cachix installation steps; done means determining whether the cache installation is actually failing and documenting a specific, reproducible cause.

I'm assuming that the cache system is not working. Looking at the installation output, it looks like a cachix installation was attempted, but considering I have been waiting about 40 minutes for the install to finish, I think something is wrong with the cache system/service. Also, I don't see cachix installed on my system like I was expecting.

Using a fresh installation of Ubuntu 22.10

Note: a multi-user installation is possible. See https://nixos.org/manual/nix/stable/installation/installing-binary.html#multi-user-installation
performing a single-user installation of Nix...
directory /nix does not exist; creating it by running 'mkdir -m 0755 /nix && chown alfredo /nix' using sudo
copying Nix to /nix/store...

installing 'nix-2.13.3'
building '/nix/store/3yc97yq64yrs0mjxy8hsdrzn9fk2np3r-user-environment.drv'...
unpacking channels...
modifying /home/alfredo/.profile...

Installation finished!  To ensure that the necessary environment
variables are set, either log in again, or type

  . /home/alfredo/.nix-profile/etc/profile.d/nix.sh

in your shell.
installing 'cachix-1.3.1'
copying path '/nix/store/bx5ikpp0p8nx88xdldkx16w3k3jzd2qc-busybox-static-x86_64-unknown-linux-musl-1.36.0' from 'https://cache.nixos.org'...
copying path '/nix/store/qmnr18aqd08zdkhka695ici96k6nzirv-libunistring-1.0' from 'https://cache.nixos.org'...
copying path '/nix/store/3zx0jnfgjvwv075ai2lkjhlsk08fixws-nix-2.12.1-man' from 'https://cache.nixos.org'...
copying path '/nix/store/vv6rlzln7vhxk519rdsrzmhhlpyb5q2m-libidn2-2.3.2' from 'https://cache.nixos.org'...
copying path '/nix/store/i37dnj0kyad5j6fmq3vfijzc62fcx1iv-nlohmann_json-3.11.2' from 'https://cache.nixos.org'...
copying path '/nix/store/76l4v99sk83ylfwkz8wmwrm4s8h73rhd-glibc-2.35-224' from 'https://cache.nixos.org'...
copying path '/nix/store/jn9kg98dsaajx4mh95rb9r5rf2idglqh-attr-2.5.1' from 'https://cache.nixos.org'...
copying path '/nix/store/pcg4cwhwnkcy7jsjd35j70zmrc9fmzas-aws-c-common-0.8.9' from 'https://cache.nixos.org'...
copying path '/nix/store/bw9s084fzmb5h40x98mfry25blj4cr9r-acl-2.3.1' from 'https://cache.nixos.org'...
copying path '/nix/store/280dqdxk41jg2axzwnxvc9hr2acvv7fb-aws-c-compression-0.2.16' from 'https://cache.nixos.org'...