Let’s say you have to be somewhere at a particular time, and you can’t be early or late. Is there always a starting time that will get you there at exactly the right moment? And no cheating like going in circles because you’re early. You have to go the fastest possible speed on the best possible route.
In theory, if you can say with certainty what time you need to be there and how long it will take you to get there, then yes. If you do not know either of those with certainty, then no, you cannot.
It’s a simple answer since the question, frankly, puzzles me. In the real world, since you cannot know with certainty how long it will take to get from A to B (because you cannot predict what will happen on that journey) then you can never predict the exact right time to leave.
The answer to your question depends on whether you are permitted to use modes of transportation that are continuous or discrete. For example, a car, bicycle, or walking has no fixed start or end time. So, assuming a perfect universe with (ha) no traffic jams or detours, and a complete knowledge of the location of your destination, your current location, and the distance between the two,you could indeed calculate the required distance, slip on the cruise control, and arrive at the very nick of time.
But…the only place you’re ever going to achieve this kind of ideal condition is rendezvousing with an object in deep space. Real life is unfortunately full of discrete events that you have no control over. One example would be a traffic light. Assume you were cruising along at the speed required to arrive at your destination at exactly the right time. You hit a red light and it delays you to the point where there is no velocity that you could achieve to get to your destination on time. “Well,” you say, “Couldn’t I drive fast enough to make the light in the first place?” Well, remember, you’re required to drive at the fastest possible speed by the conditions set up in the OP. So you can’t either dawdle or speed up.
More examples of “discretizing” events would be elevators, trains (either taking trains or waiting for them to go by), ferrys, and so on.
Note that I’m avoiding any reference to Xeno’s Paradox which would have it that you’d never arrive at your destination at all, and any mere cavilling that the real world being what it is, you could always specify “exactly the right moment” with a precision that exceeds that achievable by any known method of transport.