Normally, it should be possible to update the BIOS through IPMI even without an installed CPU, but IIRC Supermicro charges a fee for a tool doing this, and that is why it might be not possible with the MB as received.
In any case, a Celeron G6900 should have a price in the range $50 ... $80.
Unfortunately, according to SuperMicro support, this is not possible. From a support case I opened for my X13SAE-F board not booting. They have a FAQ entry saying that the board
can support 13th gen Rocket Lake CPUs with BIOS R 2.0. They just neglect to mention that it hasn't actually been released yet. I followed it up asking what my options were when and how to flash it since I only had a i5-13600K. I straight up asked if I could use a 12th gen Pentium or Celeron. Their response:
Based on the current schedule, the estimated ETA of R 2.0 BIOS will be in the middle of November. This motherboard doesn't support any Intel Celeron and Pentium CPU.
Unfortunately, this model doesn't support BIOS flash inside the IPMI due to the Intel ME firmware limitation. If you don't have any Intel Core 12th Gen. CPU on hand, please kindly contact our RMA Department for BIOS updating service.
I know there's a difference between "supports" and "absolutely won't work". It's very well possible they just haven't tested cheaper chips with the ~$500 board. I just am passing along what they said. Hopefully it prevents disappointment if indeed Celerons (and Pentiums) aren't supported...or maybe comes as a surprise if it does work.
I ended up disappointed regardless. It ended up my board was DOA. IMPI interface works, but the board never fully powers on. Immediately turns off. And that's after I convinced the wife she needed to upgrade her desktop so I could have a 12th gen CPU handy...