The Linux is remote, a node in a cluster, not a desktop in front of me, so I don’t have full control. I’m just a normal user having no super user privileges. I can only read and write within my own user space. I can only login using SSH.
CUDA 11.0.3 is installed in Linux, but cnDNN isn’t.
The graphics hardware is powerful enough that TensorFlow 2 is happy to work with.
Python 3.8.6 and pip 20.1.1 is installed in Linux.
gcc 10.2.0 is installed.
Docker is not installed.

My question is: how to install TensorFlow 2 with GPU support on Linux without super user privileges, if possible at all? Alternatively, is it possible to install Docker in my user space and then install TensorFlow 2 with GPU in Docker? The ultimate result is that I can run
python3 -c "import tensorflow as tf;print(tf.reduce_sum(tf.random.normal([1000, 1000])))"
as in TensorFlow 2 install webpage. Step-by-step instructions will be appreciated, but a link referring to an external webpage containing working  step-by-step instructions is also ok (I didn’t find it). Thank you.