Below is a brief summary on how to install basemap. I have not been successful in installing it globally. When installed in a virtual environment, there are no issues. Below are instructions for how to do so; make sure to follow and install dependencies to your virtual environment in the sequence provided.
Note: This assumes you already have Python >= 3.8 and Anaconda installed.
Basemap should successfully install this way. You will be able to access it in your virtual environment only through this method.