You could download the setup you want to install and then install it automatically without using the setup's UI:

[Net.ServicePointManager]::SecurityProtocol = [Net.SecurityProtocolType]::Tls12

Invoke-WebRequest -Uri "https://www.python.org/ftp/python/3.7.0/python-3.7.0.exe" -OutFile "c:/temp/python-3.7.0.exe"

c:/temp/python-3.7.0.exe /quiet InstallAllUsers=0 PrependPath=1 Include_test=0
I don't think it will work without admin privileges though, I tried using InstallAllUsers=0 to install it only for the current user but it is still asking for elevation.

There are some options you can use when installing it this way, here is the doc: https://docs.python.org/3.6/using/windows.html#installing-without-ui