Since you would know that light always travels at the constant velocity with respect to all frame of reference, according to relativity, whenever we are traveling at the speed of light, our time with respect to a relative rest observer would become stopped. It means that light travels with respect to all frame of reference at the light-speed, so it implies that the light from the Sun would never reach us--but sadly it would reach us within 8 minutes. How is that possible?
You have two facts.
The observer standing on Earth sees the light ray as taking eight minutes to cover the distance from the Sun.
The ray itself sees the universe as infinitely compressed so that no time elapses on it's travels (over any distance).
Both of the facts are correct. Both frames are equally valid, and physics works in both (though the zero proper-time frame of the light ray is rather boring).
The same phenomena can be observed in a less extreme way in the decay of muons created by cosmic rays.
If (and that's a big if) I understand your question correctly, your premise is that, from light's "perspective", it's we that are at speed $c$ and so our "time is stopped" relative to light's reference frame?
If this isn't your premise then I'm not sure what you're asking but, if it is, keep reading.
When you write "whenever we are traveling at speed of light", you should pause and ask "is this possible?". The answer is no, it isn't possible; there is no reference frame, in the context of SR, in which we are travelling at $c$; we literally "can't get there from here".
Put another way, there is no "rest frame" for light. It simply isn't meaningful to write or think about what the world "looks like" from light's "reference frame" since all events are simultaneous. In the 1 + 1 dimensional case, all events are also co-located, singular. No mapping is possible from that to the world as we know it.
With Lorentz transformation, you'd get dilated time of light infinite (time of rest observer divided by zero). It doesn't mean time has been stopped for a photon. It means, Lorentz transformation has failed to describe this situation in its working domain (the same is true for any theory giving you monstrously high or low number).
Relativistic physics doesn't allow you to take position of a photon. In other words, relativistic physics doesn't allow photons to be an observer. Its because a photon can see itself stationary which breaks the framework of relativistic physics. Relativistic physics doesn't allow photons to be at rest in any reference frame.