cross compiling kernel for raspberry pi 4

I am new to linux and I really need your help

I am working on project for my end of studies internship : controlling sensors and displaying the result on an LCD screen

for that I will use raspberry and create a QT application for displaying the result of the sensors.

The boot time need to be very minimal so for that I want to create a minimal kernel for my raspberri pi-4 b

I did the cross compilation for arm64:

mkdir rasp_arm64cd rasp_arm64/git clone --depth=1 https://github.com/raspberrypi/linuxsudo apt-get install qemu-system-armsudo apt-get install lzopsudo apt-get install gcc-aarch64-linux-gnucd linux/make -j8 ARCH=arm64 CROSS_COMPILE=aarch64-linux-gnu- mrpropermake -j8 ARCH=arm64 CROSS_COMPILE=aarch64-linux-gnu- bcm2711_defconfigmake -j8 ARCH=arm64 CROSS_COMPILE=aarch64-linux-gnu- Image modules dtbs

this is what I did

How can I actually make a .img file for my a bootalbe SDcard for my raspberry pi 4?

I also worked on https://www.raspberrypi.org/documentation/linux/kernel/building.md

and I added (cen someone also clarify why we need this)KERNEL=kernel8

and after that I didmake ARCH=arm64 CROSS_COMPILE=aarch64-linux-gnu- Image modules dtbsmkdir mnt
mkdir mnt/fat32mkdir mnt/ext4sudo mount /dev/sdb6 mnt/fat32sudo mount /dev/sdb7 mnt/ext4

 sudo env PATH=$PATH make ARCH=arm64 CROSS_COMPILE=aarch64-linux-gnu- INSTALL_MOD_PATH=mnt/ext4 modules_installsudo cp mnt/fat32/$KERNEL.img mnt/fat32/$KERNEL-backup.img

I got an error telling that mnt/fat32/.img no such file or directory

I tried also

$ sudo cp arch/arm64/boot/dts/overlays/*.dtb* mnt/fat32/overlays/cp: target 'mnt/fat32/overlays/' is not a directory

so I tried to create it

$ mkdir mnt/fat32/overlaysmkdir: cannot create directory ‘mnt/fat32/overlays’: Permission denied

can anyone please help me I am stuck in this error for 2 weeks now and I need to build my kernel to start working on it!

I don't know also if this version of kernel and this configuration are minimal. can I have a minimal boot time with this configuration (I think of changing the boot sequence and just enable the devices needed for my application at first but of course i don't know how to do it) If anyone can help please en-light me !! even if you just know a good tutoriel to recommand me or something..

I will be grateful if someone could help