ASUS TUF GAMING B660M-PLUS D4 – BIOS too old for i5-13500 processor

TLDR; I prepared a calculator. The main board is basically compatible with my CPU, but not with the BIOS that was delivered. The motherboard does not contain flashback.
What is the easiest option for me to install a new BIOS? Do I have any other options than buying an old Socket 1700 CPU (maybe some Celeron’s)?

long version:
Fault: On startup, the CPU lights up constantly. The computer restarts after about 10 seconds. The computer is not outputting an image via HDMI or DisplayPort.
revision:

• Error Checked LED – Indication of a CPU error
• Reinstall the CPU and the cooler. All screws are straight, and the fan locks cleanly and without much pressure
• Computer startup: identical error pattern
• Check BIOS version via barcode: 0418
• Check release date 0418 https://www.asus.com/motherboards-c…esk_bios/?model2Name=TUF-GAMING-B660M-PLUS-D4 -> Gives: 10/22/2021
• Check out newer versions from the same page: New Intels support is coming with version 1620 (08/16/2022)
• As of today, the latest version will be Build 2212 01/09/2023

This relatively shows me that the BIOS version is too old. How do I update the BIOS? (preferably without having to install other CPUs; I currently don’t have any suitable ones in my basement)

regular:
CPU: intel i5-13500 with boxed cooler
Motherboard: ASUS TUF GAMING B660M-PLUS D4
Memory: Kingston FURY Beast 32GB 3600MHz DDR4 CL18
SSD: WD_BLACK SN770 1TB High
PSU: Be quiet! Pure Power 11400 Watt ATX PC PSU 80PLUS Gold BN292

Thanks for any help!