How many millions of years did it take for this gap to be worn out of the earth's surface?
The strata cover hundreds of millions of years of deposits. The gap was "formed" in less than 2 years.
But if you assume that there is no "creator", you would no doubt conclude that it took millions of years for erosion to wear down this much rock.
Now, I presume your posted picture was meant to be some self-evident "proof" that something I said was silly. There is a reason we use language, so you can effectively communicate, something your post woefully lacked.
So, how many years would it take for man to create the Grand canyon, if money was no object and we really thought it would be cool? 100? 200? we built the Panama canal is a short period of time. We have drilled through miles of the earth. I'm betting we could pull off a grand canyon.
So, how do we know that we didn't create the grand canyon? Well, that's pretty easy, because we have records of humanity, and we see no record of it.
Oddly, there is much discussion about many of the things we find throughout the world that seem more clearly to be "man-made", but which we have no record of. Some people speculate that aliens came. Other people try to figure out exactly HOW such huge edifices might have been created, knowing what human capital existed at the time and what their engineering expertise would have been.
So, could God have created the Grand Canyon, looking pretty much like it does today, about 6,000 years ago? Well, "God" as speculated is an infinitely powerful being who can manipulate both matter and energy. So it seems clear that He could make the Grand Canyon. We could make the Grand Canyon.
Your picture shows the current state of existence of a large quantity of matter. Based on a series of assumptions on the initial state, we can put together a pretty good scientifically plausible history that is, for the most part, internally consistent. Not surprising in that whenever something inconsistent is found, we simply change our historical story. Still, somewhat remarkable that we can actually create a story with consistency -- not a necessary thing if we presume instead that it was created.
But that such a story CAN be constructed does not mean that it is an accurate historical explanation. It is merely a possible explanation.
You come by my desk, there is an empty pencil box. There are 11 pencils on the desk, two hanging over the edge. There is 1 pencil on the floor under the desk.
What is the history? Hmm. A perfectly consistent story is weaved: We see another box of pencils standing on end. The 2nd box is sitting where it would if it was previously standing up next to the first box, and fell over (it is leaning upside down somewhat balanced on some books). The pencils that are on the desk look like they could have slid out from where the box is. So the box fell over, the pencils slid out, started rolling, and one rolled off the table, where gravity (another scientific theory) caused the pencil to fall to the ground.
Except that I just staged this event. I put the pencil on the ground.
See, that is the problem with creation and with evolutionary "history". They are outside the pure realm of science, because they only provide one explanation for what we currently observe, and cannot rule out the magic of creation.