Sure, but you can't have that answer in a traditional RPG.
What you're describing is what you do in a narrative or storygame, where dramatic need eclipses verisimilitude or any objective idea of how fast FTL travel in that universe actually is. If that's what you want, fine, but I prefer drama to not be a power source in my games.
My games don't have a "story" to serve.
You seem to be conflating two diametrically opposed ways of resolving travel in a drama-centric fashion.
In what is often called "trad" or "Hickman revolution" RPGing, the GM makes a decision about what the next event/story beat will be, and narrates accordingly. An early example of this that I'm familiar with, that actually predates Hickman, is found in the example dungeon in the book What is Dungeons & Dragons, which was published in 1982. That dungeon has a "freeze frame" room - when the PCs arrive at the room, the prisoner is about to be sacrificed to the giant lizard by the evil priest. There is no "objective" timing to this - it is a GM-stipulated dramatic event, triggered by the PCs arriving in that part of the dungeon.
I think
@Red Castle is describing a similar sort of approach.
In what are sometimes called "narrativist" or "story now" games - Apocalypse World is probably the most famous; Burning Wheel is one of my favourites; 4e skill challenges are the best instantiation with the D&D-verse - the GM does not pre-author arrival just in the nick of time, or just too late. Rather, these would be success results or failure results that are narrated in response to the appropriate check(s) made to resolve the travel. For instance, rushing through the enemy complex to try and rescue someone looks like (in AW terms) Acting Under Fire (where the "fire" is
do I get there in time?). On a 10+the PC gets there in time; on a 7-9 the GM "offers a worse outcome, a hard bargain, or an ugly choice" - eg you can rescue your friend, or stop the villain, but not both (so many adventure stories features this sort of thing); on a failure the GM can makes as hard and direct a move as they like - you fail the rescue, and your friend is dead.
The two approaches are diametrically opposed because of the very different ways they locate the decisions of the participants vis-a-vis how the outcome is established. But the existence of either, or both, of them shows that it is quite straightforward to have dramatic-centric travel in RPGing.