If you have source code, QMK's documentation should tell you what you need to install and run to compile. Compilation would result in at least a ".hex" file and a few others.
If you downloaded a ready-made firmware, you should have a .zip file (or whatever) that contains the .hex file.
There should be a USB-capable bootloader on the chip. There are multiple different ones for different boards.
You would have to find out which one is used by your board and get the appropriate loader program that would talk with the bootloader. Then start that program and follow the program's instruction to load the ".hex" file onto your board.