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Disclaimer, I am not a physicist, just a guy with interest in sci-fi, science, and too much free time.
So, the answer is, yes, this is actually kind of a common theory on how time actually works. Maybe.
This has to do with physics, and the fact that no two observers have the same perfect frame of reference. For most of us humans, our frames of reference are close enough to be identical on a day-to-day basis. It's even close enough for (most) science. But it's not true on a perfect level. For instance, special relativity says that time passes differently for objects in motion; GPS satellites have to correct for the fact that their onboard clocks are experience "slower" time than us observers on Earth. Even astronauts "lose" about ~1/100th of a second for every year spent on the ISS.
What's this got to do with the future not existing, though?
So we know no two observers have a perfectly identical frame of reference - there is no objective "truth" of when something occurred. Cool. Now what? Well, what we can talk about is historic light cones. Because the speed of light in a vacuum is a universal constant, we can determine how far from you a photon departing your actions would travel. Places that photon would reach at any given point in time following your action are said to be within your historic light cone, and in common parlance, the past. The boundary of how far that photon is reaching at any given moment is, from your frame of reference, "the present". But since nothing can exceed the speed of light, it is impossible for an observer to view beyond the present, into the future.
The catch, of course, is reference frames. You used a plural - "our frame of reference", "we're blazing a trail forward" - but the reality is that each of us has a minutely different reference frame and is blazing a minutely different trail. Again, for almost any day-to-day purposes this is irrelevant... but there are certain scientific experiments which exploit or even rely on this absence of reference frame.
Cool, what about time travel again?
In my first comment above, I mentioned something called closed timelike curves. Those are an actual thing: By severely bending spacetime, you can theoretically cause a photon to "curve" around and end up at the same point in time it was produced, now in its subjective past, while mathematically not violating quantum physics.
This is where things get kind of freaky and headachy; if a photon can be sent into its subjective past, doesn't that imply a future now existing, in which that photon will be generated? The answer is, not in the frame of reference of that particular photon. A historic light cone of that photon being generated, now in that photon's future, still exists; but that photon is now generating a new, detached lightcone...
Like I said, headachy. I also have to emphasize that while the math holds up, there's ample reason to believe CTCs don't exist, chief among them that our mathematical understanding of quantum physics may still be imperfect.
tl;dr: Yes, absence of reference frames means that each distinct observer is blazing their own trail, which spreads into the "past" at the speed of light. The future, exceeding the speed of light, is unobservable. This framework does provide a mathematical concept of how you could send something into your subjective past, but such a means is still theoretical at best.
That was fascinating to read, thank you!