Unless your going on the assumption that absolutely nothing in reality can be proven, I don't see it. The number of days in a week is just a number, no matter how it came about. If we have measurements of time some number has to be attributed to things that quantify it, even if people picked a measurement based on what was convenient for them.
Ok, let's assume that time is real and not just a concept...
Imagine, it's the year 2050 and scientists have developed a technology that allows human beings to travel back in time. To test and confirm the technology, one of the scientists agrees to have himself sent back in time. He hops into the time machine, sets the date for 800 B.C. and flips the switch. In a matter of a few moments, that scientist is gone. Where is he? Well, he's back in the past, in the year 800 B.C.
Now, how does he get back? Where does he travel to? Does he get sent to the same exact spot in the universe, only 2,850 years in the past?
Since certain things that exist in 2050 AD didn't exist back in 800 B.C., will those things be able to go back in time, even though they haven't been created yet? His clothes? His shoes? His watch? Himself?
Since the time machine itself didn't exist back in 800 B.C., would that be able to travel back in time as well, even though it wouldn't have been created yet?
Can he go back in time as far as he wants? Can he go to the moment when time began? Actually,
when did time begin? If time exists, wouldn't there be a beginning to it? Ironically, what happened during the time period before time began? Could the scientist time travel to a point
before time even began?
Since time is just a concept, none of this can happen. Like I said before, without using our units of measurement, prove that time is real and not just a concept. Not even the most brilliant minds in the world can do that, which is why I believe time to be nothing more than a concept. We, as human beings, just accept time as being part of our life because that's how we were raised. We were raised to believe that when the sun rises, it's morning, and when the sun sets, it's night. We were raised to believe that there are 365 days in a year and each time our birth date passes during each year, we are now a year older, which is what we call "aging". But, what nobody can do is prove that time has actually passed when we "age". We only believe that it has because we have labeled what we call "time" with certain terms, such as seconds, minutes, hours, days, etc.
Just like the existence of a god, time can't be proven. It can only be followed, as it is how we were raised to live.