Although this question is old, it is still done by many who use MSYS2.
I've been using it this year instead of CygWin, and I'm getting pretty satisfied.
Today I had the need to install make
and did not know how and I started to search, I got to this question but it did not work, and I continued my research so I ended up reading the entire MSys2 manual and added to the knowledge collected in others posts.
Everything is very simple as always (after we've learned)
To install make in msys, just enter the msys shell and enter the commands to update the shell, this is good if you have some old installation then type the commands below and confirm for the update to be done:
pacman -Sy pacman
pacman -Syu
pacman -Su
In the above three commands, if necessary, close the window and reopen for each.
Now to install make and it works without much magic just type:
pacman -S msys/make
You already have the msys2 make available on your windows.