My preferred method of installing python gdal packages have always been with Christoph Gohlke's wheels (.whl) and pip which have recently moved to GIT Hub - https://github.com/cgohlke/geospatial-wheels
Depending on the python version you are using it might be necessary to look through previous releases to find the package that matches your OS and python version. Each python version requires a different package.
Steps:
identify python version by entering the this python command in command line
C:>python --version Python 3.13.1
Go to https://github.com/cgohlke/geospatial-wheels/releases go through the assets list and find the GDAL package that matches your python versions and download it. In this example GDAL-3.10.1-cp313-cp313-win_amd64.whl
install the python package from the download (change the file path to the downloaded .whl file from the example below)
C:>python -m pip install C:/Downloads/GDAL-X.XX.X-cpXXX-cpXXX-win_amd64.whl Processing c:\python-env\gdal-3.10.1-cp313-cp313-win_amd64.whl Installing collected packages: GDAL Successfully installed GDAL-3.10.1