You'd need to check your contract and your state law, you might be able to leave without notice.
Normally that is considered somewhere between rude and unprofessional, but in the current circumstances your old company might not mind at all. If you are furloughed you can't do any work during a 14 day notice period, so there is no reason to hold you back.
I'd say talk to the new company. Tell them that you can start at date X if you have to give 14 days notice, and ask if you could start earlier if you manage to leave without notice.
Once that is sorted and you have an offer, you can go to the old company and say ”I would like to leave. I can give 14 days notice, but I’d rather leave earlier if that is possible at all.” Just leaving without telling anyone is obviously bad. And you’d want to give enough notice that all the paperwork can be done. Let’s say first thing in the morning of the last day, or better the day before. Be prepared that they say “You can leave now, but you need to come in in five days to sign everything”.