I think you're asking why we see time as a "dimension". I take "manipulated" to mean that it's a construct of the physical reality of our universe, rather than a construct we've developed to deal with describing our lives (like morality, for instance).

The answer to that is "because of Einstein's observations of relativity and the subsequent testing of those observations", or, the relationship between space (distance, etc) and time.

If time were simply "the measurement of change" or "the separation of events", then you'd be right. It's just a construct. Not a real, tangible thing. Just a tool for us to place markers in our memories.

But relativity demonstrates that time and its passing is a real, tangible effect. The passing of time is more than just our deciding that calendars and clocks are useful.

Relativity demonstrates that time actually does pass differently in different circumstances. In the same way we can point to a physical and real "rainbow" created by light through a prism in our reality, we can also point to a physical and real dimension of time too using more advanced technology.

We know time passes slower with higher forces of gravity. We're all "time travelers", we're just typically doing it at such an incomprehensibly small difference of rate with respect to another that it seems we're locked into it. Largely we are.

But go fast, and time begins literally slowing down. Move away from gravity, time goes faster. And we've physically proved this is true. We put synced up atomic clocks on the ground, and another in space. The one in space ticked faster than the one on the ground.

We don't really know "what" time is. We've defined it, sort of, and we're all intimately aware of it. But I don't think anyone can answer that question today to any satisfactory extent.