Whether space-time and time are real or not is a debate physicists have been having for over a century but I suspect the pendulum are swung strongly towards both concepts being real.
For me there is no doubt both are very real.
The evidence comes from quantum mechanics supported by relativity.
A common misconception is the incompatibility of quantum mechanics with relativity; this is true with the scale dependent theory of general relativity but not so with special relativity.
The Schrodinger equation is based on non relativistic quantum mechanics, the Klein Gordon equation is the relativistic version of the Schrodinger equation incorporating space-time into the equation.
The Klein Gordon equation was originally a nightmare for physicists; it predicted negative probabilities and negative energies.
The latter provided a clue to antimatter where the energy levels are below a ground level through an earlier attempt of combining special relativity and quantum mechanics through the Dirac equation.
The negative probabilities problem was solved by considering ψ as being a field in the Klein Gordon equation whereas in the Schrodinger equation it is a wavefunction.
The field is an operator which can create and destroy particles.
From this arose quantum field theories where a vacuum is space-time in the lowest energy level and with it came a prediction space-time can exert pressure which was confirmed by the
Casimir effect.
It’s very difficult to argue about space-time being a human construct when it can exert pressure.
The issue with time can be dealt with non relativistic quantum mechanics.
The Heisenberg uncertainty principle states;
ΔxΔp ≥ h/4π
h is Planck’s constant, Δx and Δp are the uncertainty in the measurements when the position and momentum mathematical operators X and P applied to the eigenvector |ψ> giving the eigenvalues x and p which are the measurements or observables according to the equations X|ψ> = x|ψ> and P|ψ> = p|ψ> respectively.
The Heisenberg uncertainty principle can be expressed differently using energy and time.
ΔEΔt ≥ h/4π
Here E is the eigenvalue of the Hamiltonian operator H where H|ψ = E|ψ>.
There is a problem with t as there no mathematical operator T such that T|ψ> = t|ψ>.
t is not an uncertainty in the measurement but a time interval which depends on a physical process such as the energy level of an excited state depends on how long it is in that state.
This connection between energy and time makes it difficult to conclude time is simply a human construction.