I assume you are working at a exceptional company (FAANG level at least) since your management team is capable of estimating time required for bug fixes in such

I assume you are working at a exceptional company (FAANG level at least) since your management team is capable of estimating time required for bug fixes in such a precise manner. But seriously, the best management I've seen had a pretty good way of communicating what was important to work on. For something like that they would simply have emailed the dev team and stated that "bug X is an absolute release blocker" along with a list of engineers in charge of leading the fix (said engineers would have been contacted privately and whatever tasks they had deprioritized). Then the email threads would be used to share the latest details on the investigation. You can't put a hard deadline on something like a bug fix, but you can maximize your chances of meeting that deadline by making sure the right folks are 100% focused on that fix. Now, is your management technical at all?