My cold water valve is frozen open, water is leaking from the spout and the building won't turn off my tier for 2 weeks.
If you had an old faucet with just a valve stem and flat washer, possibly. You could open the old valve and the new valve stem and remove the old one. The water would gush out but when you inserted the new, open valve stem, water would be diverted to the spout and you could probably get it done.
On the newer faucets with cartridges, the cartridge needs to be fully seated to work and they have a number of "o" rings and seals that would be dislodged by the water gushing out. Plus, once they're seated, they have to be secured by a nut or lock ring which wouldn't be easy to do while holding the cartridge in place.
Try to carefully free up your cold water shutoff with some vinegar or lime-a-way.
I did, few times, mount some plumbing elements under pressure. And never failed (other than getting wet myself).
But I always did have the main valve accessible in a timeframe not alowing a damaging flood.
The tricky part is aligning the threaded pieces right while fighting the water pressure at the same time.
Opening nearby faucets to lower the water pressure sometimes helps a lot and sometimes not much.
IF you can convince and synchronize all of your lateral and downstairs neighbors to turn on all of their faucets and tubs (both hot and cold) at the same time for 30 minutes then the water pressure has the potential to get low enough for you to be successful. If you live on the lowest level then this will not work.
Just make sure to open your taps as well to verify that the water pressure is low enough to perform the work.
This of course assumes you know exactly what you are doing and are able to complete the job within the anticipated timeframe.
Realistically, just wait for the water to be shut off.