If we could travel instantaneously between two points in the cosmos, it would indeed have implications for time dilation. Time dilation occurs due to relative motion or differences in gravitational potential, and it is a consequence of the geometry of spacetime.
In special relativity, time dilation arises when an object moves relative to another object at speeds close to the speed of light. The faster an object moves, the more its observed time slows down relative to a stationary observer. However, if instantaneous travel were possible, it would imply that there is no relative motion between the starting and destination points, and therefore no time dilation due to relative velocities.
Similarly, in general relativity, time dilation arises due to differences in gravitational potential. Clocks in stronger gravitational fields tick slower compared to clocks in weaker gravitational fields. If we could instantaneously travel between two points, we would essentially bypass the gravitational field and not experience the time dilation associated with it.
However, it's important to note that the concept of instantaneous travel is purely hypothetical at this point. no known method or technology allows for such instantaneous transportation. Our current understanding of physics, as described by relativity, suggests that time dilation is a fundamental aspect of spacetime and would still exist for objects and observers in relative motion or subject to different gravitational potentials.