Now that the new anaconda individual edition 2020 distribution is out, the procedure that follows is working:
Update conda in your base env:
conda update conda
Create a new environment for Python 3.8, specifying anaconda for the full distribution specification, not just the minimal environment:
conda create -n py38 python=3.8 anaconda
Activate the new environment:
conda activate py38
python --version
Python 3.8.1
Number of packages installed: 303
Or you can do:
conda create -n py38 anaconda=2020.02 python=3.8
--> UPDATE: Finally, Anaconda3-2020.07 is out with core Python 3.8.3
You can download Anaconda with Python 3.8 from https://www.anaconda.com/products/individual