We roll our own initramfs, rather than the Debian one which is quite bloated. See osmc/package/kernel-osmc/initramfs-src at master · osmc/osmc · GitHub.
The main init script is: osmc/init at master · osmc/osmc · GitHub
Building is very easy. It can be done on any OSMC device
sudo apt-get update
sudo apt-get install armv7-toolchain-osmc build-essential git (for pi2/pi3)
git clone https://github.com/osmc/osmc
mount --bind $(pwd)/osmc /opt/osmc/armv7-toolchain-osmc/mnt
chroot /opt/osmc/armv7-toolchain-osmc
cd mnt/package/kernel-osmc/initramfs-src
make cpio DEVICE=rbp2
This will generate an initramfs.gz