Instead of running your entire script as root, you could use sudo in your script to run only the pacman command as root:
#!/bin/bash
mkdir ~/Documents
sudo pacman -S firefox
This way the Documents/ folder will be created in your user's home directory and then you will be prompted for the root password in order to execute the pacman command as super user.
Note:
As @jeremysprofile stated in the comments:
You can definitely make folders as root
I suppose the problem is that you expect the Documents/ folder to be created inside your user's home directory. However, if you run you script as root, ~ expands to the super user's home directory: /root/. So this is where you will your Documents/ folder created with your current script.