Having problem while downloading OpenMC with Anaconda after successful download of conda, mamba, & mamba install OpenMC but still can't proceed to "install OpenMC" having error message saying: " OpenMC does not exist" what should I do?

Sorry, I have not much experience with conda installation, So I think I only recommended you to follow the instructions >> Installing on Linux/Mac with Mamba and conda-forge
Disclaimer: I am using miniconda at that time and not using other conda installation, so I have no experience with other installation methods.

Have you add conda-forge to your conda channel? openmc can be installed via the conda-forge channel with mamba.
conda config --add channels conda-forge

Since conda create dedicated openmc environment openmc-env, then if you think something is not work properly, you could (at last) delete this environment and start again following the instructions.

conda env list
conda deactivate # to deactivate current env 
conda remove --name openmc_env --all # if openmc_env is your openmc environment name

Also make sure that your new openmc environment use python 3.10+ version because the latest openmc version supports Python 3.10+.