p10k doesn’t require omz. You can install it by itself, the instructions are right there on the Github repo.
On a new computer, I: git clone my dotfiles repo. Run the install script which symlinks all the relevant files, clones any needed repos like asdf, fzf, p10k, sources the .zshenv and .zshrc, runs asdf installs for my required tools, installs homebrew if on macOS, runs brew bundle to install everything else.
Homebrew takes the longest. The rest is done in a few seconds.