That really depends on what you mean with real thing, I would say our understanding of time and space is heading towards them being emergent phenomena and not fundamental ones. As far as we know, there is no thing in the universe called the time that you can just measure, you can only look at the ordering of events. And then we invent a variable called time that lets us express the laws of physics reproducing the observed events in a simple way, but that is much more a convenient mathematical and everyday tool than a real thing than one usually realizes.

Time is absolutely a construct, just like the iPad I’m typing this on is a construct. I really can’t be sure it exists, but the model I have in my head that I’m tapping on a large flat surface with my fingers agrees with my observations. If in my next tap I get a painful burning sensation in my finger and I hear the fire alarm go off I may need to change my model to consider that I was mistaken and I may be touching a what appears to be a flame instead.

Isn't time "merely a man-made method of measuring the motion of the Earth around the Sun?"