I've found on both Manjaro Arch derivative and now Arch I have had a recurring problem of a black background on log in. Its an intermittent fault that happens about 30% of the time. I have spent quite some time trying to solve it. Here's a few observations. They are largely observational based on my experimentation and researching forums.

(1) Changing the splash screen to "none" under settings/appearance may significantly reduce the frequency of black backgrounds appearing.
(2) I found an external wifi dongle caused the problem to increase. Unplugging it on start up significantly reduced the frequency of black backgrounds. Maybe you have something plugged in? Maybe try unplugging it and see if it helps?
(3) For some people but not myself loading drivers early fixed the problem. It did not for me but your outcomes may vary. One example of how this can be accomplished using NVIDIA drivers is here. It assumes you have loaded the NVIDIA drivers first. Also make sure you know which drivers are on your system before proceeding. They may not be NVIDIA.

https://www.youtube.com/watch?v=_397h9ucp5A

(4) Changing the kernel. I tried moving to Zen and it did not solve the problem but apparently some have had results from moving to LTS or Zen, etc. DON'T do this if you don't know what you are doing and have not backed up your OS and important files! Fair warning!

https://www.youtube.com/watch?v=lMlQEgOexN4

I can't guarantee this will help but it "might" either reduce the frequency or maybe even solve the problem for you. Good luck.