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It's a mathematical construct that is a core part of the theory physicists use to make highly accurate predictions about many of the low-level dynamics of reality.

It seems to usually be visualized as 2d plane-like sheet that can oscillate, and those oscillations represent particles. In reality it should be 3d, but that is much harder to draw.

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So if objects are just perturbation in a field, and field is a mathematical construct, just like the concept of a number, or a line or a circle, then isn't it meaning less to look for a start for the existence of a field, and hence the whole universe?

No, for a couple of reasons. It's a mathematical construct used to describe observed phenomena, the phenomena itself isn't necessarily that similar to the construct. Further, it may be a terrible description.

A sinus is a field, deductively reduced to lower dimensions, e.g. a slice cut of a sound wave. Waves on the sea form a wave field, figuratively, and it extends to the bottom of the sea. Whereas a quantum field is a consequence of the Schroedinger Wave equation positing that the potential to observe a particle is distributed in space. As far as I know that's purely virtual, because observation of the particle collapses the potential. The crux is, the observation is not exact; The location of the particle is a probability distribution over a field as well. So ... it's fields all the way down. I'm not an expert, just stipulating.

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