You need to use Yocto in order to rebuild the rootfs image with a custom recipe which will install your bin file in the /lib/firmware folder.
Then flash this new rootfs image in the module using fastboot.
Also, some well-known firmware binaries (e.g. for WiFi chipsets) can be easy added to the rootfs images (in /lib/firmware) by adding the following line into the image recipe (e.g. meta-swi/meta-swi-mdm9x15/recipes-core/images/mdm9x15-image.inc):
IMAGE_INSTALL += "linux-firmware-XXXXX"
Where “XXXXX” is the name of your firmware package.
IMAGE_INSTALL += "linux-firmware-ath6k"
this will add all the firmware binary files for the Atheros WiFi chipsets (AR6XXX series) in the /lib/firmware.
List of firmware packages supported by the kernel is available in this yocto folder: