Download the Raspberry Pi OS Lite 64-bit image, burn it to an SD card, boot your Raspberry Pi with it and follow installation instructions.
sudo apt update
sudo apt upgrade
sudo reboot
sudo raspi-config
and set everything according to your needs. Note: if you're going to
use a VNC server, don't set it up just yet.
sudo apt install lxqt-core xinit
and then reboot, login and
startx
sudo apt install realvnc-vnc-server
and set it up via
sudo raspi-config
sudo apt install lightdm
sudo apt install rpd-plym-splash
Create the image file that's going to be used as a splash screen and save it as splash.png into your home directory. Then proceed to configure it as follows:
cd /usr/share/plymouth/themes/pix/
sudo mv splash.png splash.png.ORG
sudo cp ~/splash.png .
sudo update-initramfs -u
sudo reboot
Tested on a Raspberry Pi 3B with Raspberry Pi OS Lite 64-bit, kernel version 6.1, Debian version 12 (bookworm).