

Does the Surface Go have a SSD in it? And/or can you install a SSD into it? The specs do imply that it supports SSD so you should at least have a port in there for that. If so, as long as you have a spare machine you can install the Surface’s SSD into another system, then install Linux Mint normally there, then re-install the SSD back into the Surface Go.
I’ve never done that but it’s been mentioned a few times in the Linux Mint forums so apparently that is a roundabout way of installing on a machine without working USB ports. e.g.
https://forums.linuxmint.com/viewtopic.php?t=388243
https://forums.linuxmint.com/viewtopic.php?t=361542
Not sure how well Mint works specifically on Surface Go but it’s worth a try, most likely you’d use the same steps to install other distros on there.
EDIT: Without a spare system you might be able to download then write the Mint ISO onto a second partition inside Windows and boot from the Mint installer partition afterwards. Not sure how well that would work but someone else in the forums mentioned it https://forums.linuxmint.com/viewtopic.php?t=369154
Yikes! Yeah if the SSD storage isn’t easily accessible then it’s not worth the disassembly headache.
If that is the case then OP’s only option is to try writing the bootable ISO onto a second partition on the current drive while in Windows and boot off that partition… assuming getting the USB port repaired is a no-go.