Archlinux user here (Manjaro is based on Archlinux). TensorFlow with GPU support is a supported package you can install it with all it's dependencies in a simple command with Pacman. But you don't want to do that the same way you don't want to compile TensorFlow. It is better to use an official docker image because they include all the dependencies, even the optionals as nccl 2.0. You forgot to install it, and it is speed up if you use more than one GPU. Just use the official docker image and forget all the burdensome of configuring everything.

P.S. well you need to install docker with Nvidia support, but you can use it in the future for other things. This is also a couple of packages in Pacman (maybe Nvidia docker is in air, I don't remember now).