Disclaimer
I will be honest in saying that I have no idea how to even start on this problem as I have not read up much about hardware issues. Often in Manjaro, if it does not work out of the box, it won’t work at all. But to not discourage you from using Linux, there is a few things you can try to fix this issue.
Questions
First off, have you been able to get the microphone working on Manjaro before? If not, have you had it working on another Linux distro? If not even that, have you had it working on Windows? (If it didn’t, the mic might just be broken.)
Secondly, is it the built-in mic that isn’t working or a headphone mic? If it is one, try whether the other one does work.
Install options
Then some installer options. Pulseaudio is known to not have all the features you would like from a sound manager. You could try installing Pipewire. This is an alternative and more modern audio processor. It is still in active development, but if Pulse isn’t working, Pipewire might (it did for me when my audio glitched). Note here that Pipewire is less stable (although I haven’t experienced much issues with it) and there is less documentation available. See this post on how to switch PA to Pipewire:
Finally, it could be that the driver is only later included into the kernel. If that happens to be the case, you could try installing the latest (stable) kernel with:
sudo mhwd-kernel -i linux515
Wrapping up
Don’t forget to reboot after installing pipewire or the new kernel.
Please let me know which of these options you tried and what the results were. Best of luck!