I had a similar issue when mounting an R620. They make rail depth adapters that will take care of that. I used these StarTech.com Rail Depth Adapter Kit for Server Racks - 4 in. (10 cm) Rack Extender - 1U (RDA1U)
There are extension brackets, like this one: https://www.amazon.com/StarTech-com-Depth-Adapter-Server-Racks/dp/B01GGKM4S8
I had that rack, used StarTech's spacers to fit a larger-depth switch.
When I replaced that rack, I got this deeper one with an open back and mounted it on 2x4 spacers to provide a bit more space in back.
https://www.amazon.com/StarTech-com-Depth-Adapter-Server-Racks/dp/B01GGKM4S8
These will work for you.
I've had good luck with offset brackets like these for similar jobs: https://www.amazon.com/dp/B01GGKM4S8/
Amazon carries StarTech and Tripp Lite branded recessing adapters and front panels.
Front panel with key lock: https://www.amazon.com/StarTech-com-Rack-Mount-Security-Cover-Compatible/dp/B084PBTJ7J/ref=sr_1_4?dchild=1&keywords=3U+rack+mount+front+panel&qid=1615498953&sr=8-4
​
Note: IT rack standard cage nuts will be required.
pg. 9 https://www.supermicro.com/manuals/chassis/1U/SC813.pdf
Tells you how to adjust your rail length. If your frame is still to short front to back, you might need these
https://www.amazon.com/dp/B01GGKM4S8/ref=twister_B07J2JQRVS?_encoding=UTF8&psc=1