"Just take a guess - we have to have a number in this box by the end of the meeting". I was literally just told that yesterday. No one else who would look at that number will know it was a totally random guess pulled out of thin air to satisfy ceremonial box-filling. They will treat it as an estimate, and make plans accordingly.
And if you make up a number that is too obviously small or exceeds some unspoken upper bound, you'll be asked to re-estimate anyway. Sometimes the best way to respond to that is to finesse the discussion into coming up with a number that, while it will have no relationship to the actual effort, at least reflects what the stakeholders hope and desire it to be. At that point the team, if they are smart, will examine scope and re-plan to come up with some level of effort that they are confident can be done in the time hoped for.
In other words, get the people who want a number to tell you what number they want, then use your best efforts to scope the effort to one you can be pretty confident will fit.
Unfortunately, that seems to be the norm in almost every place that I'm familiar with.