gm techniques – How to reveal a time limit without videogaming it?

I am under the impression (so correct me if I’m wrong) that having a close time limit on objectives could be fun if there is not an abuse of the game mechanic.

So one hand, I want my players to find out about this time limit in the right moment:

Oh no, the truck where we hid the MacGuffin just left west, that’s the direction of the
bridge that was blown up! And in the foggiest day! Let’s us hurry up pals!

But on the other hand I don’t want to video-game the event* or spoonfed them the info. The truck is going to leave at 9, and crash at 11 if nothing is done. Only the guard and some employees know this. If my players think getting a drink after a rough day is more important than taking care of the MacGuffin, that’s part of TRPG.

Still I’d like to give my players as many chances as possible to find out there is a time limit, or to connect the dots.

DM: So the guard tells you that truck just left to another town via West Street, the
unique, long street that reachs out of the city.

Player: (Doesn’t remember the bridge is west) Mm okay, maybe we could find out tomorrow
where it’s headed.

This is even trickier for events the party doesn’t know about, BBEG plans, rituals, man-made catastrophes (“Hey let’s open this cursed ancient tomb in the name of archeology”). In this case it’d feel even more unfair, as the players didn’t get to make any decision, they were just slow or oblivious, and we completely miss on the adrenaline rush .

How can I improve the odds of players finding out about time-sensitive events at the right moment? Better even if they are slow or dense that day.

*Where the event doesn’t happen if the player character is not there.