If you cannot reach where you are not (yet) unless you move thither at a velocity of no greater than c, you cannot so much as get to the far end of the street three dimensionally. Your journey takes time, so you must move four dimensionally. In fact, according to the Special Theory you move at speed c anyway, with one of the components of your motion being through time, so even if you sit still and do not reach the gate, you must do so at the speed c.
In any number of dimensions, if we are to reach the end of the universe at all, there first has to BE an end. Since we cannot be sure that it is meaningful to speak of the end of the universe, and if so, in what terms, we cannot answer that question.
Do you suppose that you could rephrase it in terms that we could answer?
Please let us know if you succeed.
Cheers,
Jon