Yes, as JRobert pointed out, I have no doubt - it is possible!
You need just 3 things:
- a Bootloader that supports uploading the firmware via I2C
- an Upload-Software that supports uploading the firmware to the bootloader mentioned in 1.)
- an physical connection from the system the upload software is running on to the actual I2C bus of your device
Actually the physical interface is not the problem - there are USB<>I2C interfaces available widely, you can also re-use an arduino itself to be such.
Let's look at the bootloader.
Actually I found a german site that claims having a working I2C bootloader for Atmega8 including an upload tool (use Deepl.com to translate it). It may or may not work for other Atmegas as is.
There is also another project at github.
There will be more if you google for it. Actually I have not investigated any of them.
But chances are good than any of those might work for you.