By combining the hints from the other answers and reading through the documentation, I found a nice way to do exactly what you want that should work well in a CI system or in a Docker container or on a developer machine if they haven't already installed python3.x via Apt or Yum or Homebrew.
Assuming you have all the dependencies required to build your desired version of Python 3.x (anything above 3.4 requires some extra packages the pyenv-installer doesn't always warn you about), you can run the commands below to get a new system wide Python that should be executable by all users, which makes it easy to pass to virtualenv creations with python3.6 -m venv yourvenv
.
curl https://pyenv.run | bash # or
wget -O - https://pyenv.run | bash
export PATH="$HOME/.pyenv/bin:$PATH"
$(pyenv which python-build) 3.6.10 /usr/local/
which python3.6
python3.6 --version
# If you get an error running the above commands, it probably means
# /usr/local/bin isn't in your PATH yet
# on Debian/Ubuntu and maybe others the /etc/environment or
# /etc/login.defs file puts it in the path when a user logs in
echo $PATH
export PATH="/usr/local/bin:$PATH"
python3.6 --version