From the Pi Website...
The bootloader EEPROM image contains an embedded configuration file to define the boot behaviour (e.g. selecting between SD, network and USB boot).
https://www.raspberrypi.org/documentation/hardware/raspberrypi/booteeprom.md
That splash screen can only be disabled in the config.txt located in the Bootloader in the EEPROM.
Here's the Steps i used (explained as simply as i can) to disable it.
STEP1: log into your Raspberry Pi via Terminal SSH (i used PuTTy) default login is pi .. password is raspberry
STEP2: type (or copy'n'paste) this .. vcgencmd bootloader_version to display the version and date of the bootloader you are using. eg. mine is Sep 3 2020 13:11:43
STEP3: type (or copy'n'paste) this (if your bootloader date is different to mine, then you'll need to change pieeprom-2020-09-03.bin to the date of your bootloader. format is YYYY/MM/DD)
cp /lib/firmware/raspberrypi/bootloader/beta/pieeprom-2020-09-03.bin pieeprom.bin
STEP4: type (or copy'n'paste) this .. rpi-eeprom-config pieeprom.bin > config.txt
STEP5: type (or copy'n'paste) this .. cat config.txt
STEP6: you should see something like this below ... and what you need to change is DISABLE_HDMI=0 to DISABLE_HDMI=1
[all]
BOOT_UART=0
WAKE_ON_GPIO=1
POWER_OFF_ON_HALT=0
DHCP_TIMEOUT=45000
DHCP_REQ_TIMEOUT=4000
TFTP_FILE_TIMEOUT=30000
ENABLE_SELF_UPDATE=1
DISABLE_HDMI=0
BOOT_ORDER=0xf41
STEP7: type (or copy'n'paste) this .. sudo nano config.txt
STEP8: edit DISABLE_HDMI=0 to DISABLE_HDMI=1 .. then on your keyboard press CTRL O, then ENTER and then CTRL X
STEP9: type (or copy'n'paste) this .. rpi-eeprom-config --out pieeprom-out.bin --config config.txt pieeprom.bin
STEP10: type (or copy'n'paste) this .. sudo rpi-eeprom-update -d -f ./pieeprom-out.bin
STEP11: You will now see the following message
BCM2711 detected
Dedicated VL805 EEPROM detected
*** INSTALLING ./pieeprom-out.bin ***
BOOTFS /boot
EEPROM update pending. Please reboot to apply the update.
STEP12: Last Step .. type sudo reboot
When the Raspberry Pi reboots the bootloader Splashscreen is gone.
To re-enable the splashscreen for diagnostics .. just redo all the steps above changing DISABLE_HDMI=1 back to DISABLE_HDMI=0
cmdline.txt
because that is for the linux kernel.