You can go somewhat negative and be fine. If you go too low, some things stop getting paid, but shouldn't impact a new airlibe much. You will get a bankruptcy warning if you go low enough, probably at least 10 million in the hole in this world by now. You then have 7 real life days (about one game year) to resolve it. Assuming no c/d checks are due soon and you've set up a soon to be profitable operation, you'll be fine.
On that note, if c/d checks are due they will not be done and a death spiral will be in your future.