Since February 2017, you can install pygobject directly through pip: pip install pygobject. It requires some packages to be installed though.

Before that, it took a while, but it was possible to install pygobject with pip, since this commit.

pygobject wasn't on pypi though, so you had to specify the git or tarball URL:

• git+https://git.gnome.org/browse/pygobject
• https://download.gnome.org/sources/pygobject/3.22/pygobject-3.22.0.tar.xz

The latter only works with pygobject 3.22+, which should have happenned around mid-september 2016. (3.21.1 should be the first pip-installable development release)

For windows

1. Go to http://www.msys2.org/ and download the x86_64 installer
2. Follow the instructions on the page for setting up the basic environment
3. Run C:\msys64\mingw32.exe - a terminal window should pop up
4. Execute pacman -Suy
5. Execute pacman -S mingw-w64-i686-gtk3 mingw-w64-i686-python3-gobject
6. To test that GTK 3 is working you can run gtk3-demo
7. Copy the hello.py script you created to C:\msys64\home\<username>
8. In the mingw32 terminal execute python3 hello.py - a window should appear.

For ubuntu / Debian

Installing the system provided PyGObject:

1. Open a terminal
2. Execute sudo apt install python3-gi python3-gi-cairo gir1.2-gtk-3.0
3. Change the directory to where your hello.py script can be found (e.g. cd Desktop)
4. Run python3 hello.py

Installing from PyPI with pip:

1. Open a terminal and enter your virtual environment
2. Execute
   sudo apt install libgirepository1.0-dev gcc libcairo2-dev pkg-config python3-dev gir1.2-gtk-3.0
3. Execute pip3 install pycairo to build and install Pycairo
4. Execute pip3 install PyGObject to build and install PyGObject
5. Change the working directory to where your hello.py script can be found
6. Run python3 hello.py

You can read more here

Upstream PyGObject just does not support this. See the PyGObject win32 project or the MSYS2 project to get it easily.