Suppose you have nothing, but only a thing X which doesn't change at all, is there time? How would you say how many seconds/units of time have passed when there is only the thing X i.e. static too, and not any reference (like speed of light is constant/cesium atom) or any universal clock or absolute time-line. So would time be fundamental in such a scenario, or rather time doesn't seem to make sense without any sort of change then, or does it make sense without any change at all?
How could you know? Serious question.
We think the universe began as 'one thing', a singularity or very close to one, at a quantum scale. So in a very real sense, all being and time are happening to 'one thing'.
And just like you can get particle-antiparticle pairs from 'empty' space, we think all particles had an antiparticle in their past in order to balance the quantum 'budget', but the antiparticles decayed or were consumed by a CPT-violating process. That is matter, any matter, is involved in a long story that relates it to the whole universe (Conformal Cyclic Cosmology relates this to all matter decaying to photons, which don't experience time because of lightspeed). Even once created, properties like angular momentum are related to the universe's rest frame.
Quantum properties are really properties of systems isolated from the environment, over some time scale. When there is no way for the universe to keep track of them, their conjugated variables like position and momentum become uncertain (mass-energy will be having gravitational effects, putting a constraint on that).
I'd suggest the only possible isolated 'thing' wouod have such massive uncertainty it could be anything:
'In the begin there was nothing, which had no way to tell what was there, so it exploded'.
The answer to this question does not come under mere physics. Since change happens while thinking, I wouldn’t like to use even the term ‘get an answer’. In this case I would like to use the term ‘reveal the answer’. If you believe or not, that there is nothing else anywhere, time [as we feel (also in any form) by comparing changes] can’t exist. The one without a second or the Ultimate truth or Pure Consciousness or Brahman is that only thing. We feel that everything else is made of tiniest particles and is always changing.
According to modern physics, every object in the Universe exists in a 4d volume we call spacetime. Your hypothetical unchanging 'thing' would, assuming it is part of the Universe, follow a trajectory in spacetime as much as any other object would. From moment to moment the object itself might be unchanged but its position in spacetime would not be. Time would be unmeasurable without change, but it would be mistake to conclude there is 'no time' simply because you cannot measure it.
You say in your comments that the question 'isn't just restricted under the modern physics view.' If you are ignoring physics then you are entering the realm of imagination, and therefore you can imagine the object in any other universe with any other properties you care to give to it. For example, you might imagine a universe with only two spatial dimensions. You can try to imagine a universe with or without time, but I put it to you that it is the properties of the imaginary universe that determine whether time exists, not the properties of an object within that universe, since we know that in our universe time exists regardless of whether the objects we contemplate are unchanging.
However, I also suggest that it is not possible to maintain a meaningful concept of a universe without time, for when you say that an object exists or is unchanging you are inevitably confronted by temporal considerations. If I ask you to define what you mean by 'exists' you will eventually have to recognise that the word implies an aspect of persistence, which unavoidably relies on a concept of time. Likewise if I push you to explain what you mean by 'unchanging', you will eventually have to use phrases such as 'never changes' or 'is always the same' which again invoke the idea of time.