Time exists in physics, but the flow of time does not. Physicists do not understand the flow of time. In any given coordinate system, we can be at rest in space, but in that same coordinate system, we cannot be at rest in time. Time has this qualitatively different feature. It progresses.

This movement is currently ignored in physics. The relativistic transformations show that rotations in space-time wind up converting spatial coordinates into time, and time into space. But the space time diagram does not include any sense that time flows, that it is different. It has no special time location for "now" -- a moment of time that is central to our sense of reality because it divides that reality into two realms: that which we cannot influence, and that which we can.

Here is a quote from my upcoming book Now - The Physics of Time: "Brian Greene in his book The Fabric of the Cosmos suggests that relativity “declares ours an egalitarian universe in which every moment is as real as every other.” He says that we have a “persistent illusion of past, present, and future”—a perspective reminiscent of Augustine. He concludes that because relativity doesn’t discuss the flow of time, such flow must be an illusion, not part of reality. To me this logic is backward. Instead of insisting that theory explain what we observe, this approach implies that observations must be twisted to match the theory."

Einstein despaired of his inability to explain the flow of time. But Einstein, despite his despair, moved forward and showed that the rate of the flow of time depends on both velocity and gravity. That suggests strongly that the flow of time does not originate in the human mind, but has a true external physical reality.

Another quote from Now: "Space and time together provide the stage on which we live and die; it is the stage upon which classical physics makes predictions. But until the early 1900s, the stage itself wasn’t examined. We were supposed to notice the story, the characters, the plot twists, but not the platform. Then, along came Einstein. His great genius was in recognizing that the stage was within the realm of physics, that time and space had surprising properties that could be analyzed and used to make predictions. Even if he despaired of understanding now, his work is central to our understanding. Einstein gave physics the gift of time."

Your question is very deep. We need to think about the origin of time's flow. Einstein opened such questions to physicists.