Just throwing some random ideas out...
TCP over file tunnel? https://labs.withsecure.com/tools/tcp-over-file-tunnel or the similar https://blog.adamfurmanek.pl/2022/11/12/availability-anywher...
Or maybe establish a named pipe (https://learn.microsoft.com/en-us/windows/win32/ipc/named-pi...) on the Windows host, and try to access and proxy through it on the guest? (https://shvechkov.tripod.com/nptp.html) Never tried, don't know if that would work.
Or a similar idea is to make a virtual serial port (COM port) between the two and try to proxy internet over that using PPP, like in the dialup days: https://docs.oracle.com/en/virtualization/virtualbox/6.0/use... https://tldp.org/HOWTO/PPP-HOWTO/direct.html https://www.vader.dk/index.php?/archives/13-VirtualBox-guest...
If you can set up some sort of connection like that, you might be able to use putty or telnet to redirect network traffic on the guest through the connection
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But overall this is probably a really good way to piss off your IT department. It's a lot of hassle just to get a Linux box with internet access... why are they making you jump through so many hoops to get a VM connected to the internet?
Alternative idea: turn on the hotspot on your phone and just connect to it from the Linux guest
Alternative idea #2: Just use Windows Subsystem for Linux
Alternative idea #3: Put Linux on a USB drive and boot straight from that (if you can) instead of booting into work's Windows (just borrowing the laptop hardware)
Alternative idea #4: Plug another USB wifi stick into the host and have it share its connection there, connect to it from within the guest using the other wifi chip. Technically you're not routing traffic through the VM, one radio is broadcasting and the other is independently receiving...