Impossible deadline experience?
A few, but this one is more recent (and not mine, yet)

Company has plans to build a x hundred thousand square feet facility (x = 300, 500, 800 depending on the day and the VP telling the story)

1. Land is purchased, but no infrastructure exists (its in a somewhat rural area, no water or sewage capable of supporting such a large facility)
2. No direct architectural plans (just a few random ideas about layout, floor plans, parking etc)
3. Already having software dev meetings in attempt to 'fix' all the current logistical software issues we have in the current warehouse and not knowing any of the details of the new facility.

One morning in our stand-up, the mgr says

Mgr: "Plans for the new warehouse are moving along. We hope to be in the new building by September."
Me: "September of 2022?"
<very puzzled look>
Mgr: "Um, no. Next year, 2021"
Me: "That's not going to happen."
Mgr: "I was just in a meeting with VP-Jack yesterday. He said everything is on schedule."
Me: "On schedule for what?"
<I lay out some of the known roadblocks from above, and new ones like the political mess we will very likely get into when the local zoning big shots get involved>
Mgr: "Oh, yea, those could be problems."
Me: "Swiiiiishhhhh"
Mgr: "What's that?"
Me: "That's the sound of a September 2021 date flying by."
Mgr: "Funny. Guess what? We've been tasked with designing the security system. Overhead RFID readers, tracking, badge scans, etc. Normally Dan's team takes care of facility security, but they are going to be busy for a few weeks for an audit. Better start reaching out to RFID vendors for quotes. Have a proposal ready in a couple of weeks."
Me: "Sure, why not."