In modern physics, "time" is considered an intrinsic part of the dimensions of the universe.
It's called space-time for a reason you know.
This is simply not true. It is quite radically incorrect for a number of important reasons, some of which are actually relevant to this discussion.
First, if one had to characterize “time” in modern physics in such a manner as you did, one would say that it is a parameter, not a coordinate or dimension. Not only are vast amounts of research and study in physics devoted to non-relativistic physics (e.g., quantum mechanics and non-relativistic quantum field theory, thermodynamics, statistical physics, etc.), but even in relativistic (“spacetime”) physics, time is still introduced as a parameter.
Second, and perhaps more importantly, Classical Newtonian physics, the spacetime of special relativity, and the spacetime of general relativity all share the same spacetime manifold. Where they differ is the additional structure this manifold is equipped with, i.e., the geometry of these spaces. Classical Newtonian mechanics, for example, is built out of a Galilean spacetime, both of which (the Galilean and Newtonian spacetimes) constitute an ℝ4 manifold identical to the manifold at this level of relativistic spacetime. But in Classical Newtonian mechanics, the spacetime is decomposed into the product spaces 3 x 1. Indeed, if you take sections in Galilean spacetime that are simultaneous to be fibers with time as the base manifold of the total space of the vector bundle of the topological product space, then you can construct Newtonian spacetime from the total space of the vector bundle of Galilean spacetime by introducing “curvature” into these sections using Newtonian equations of motions written with the Christoffel (affine) connection.
Put more simply, both Galilean spacetime and Newtonian spacetime are 4D and have more in common with the spacetime of special relativity (which is also a 4D manifold, but now can be constructed without the product topology using the metric tensor with the appropriate signature/sign convention). In general relativity, the gravitational interaction neither determines nor is limited to four dimensions. In general relativity, the metric (which, put simply and only somewhat naively, determines the geometry of a space) is dynamic. This is another way of saying that the distances between points varies
in time.
Which brings me to point 3, which is that time plays a double role in the spacetime of general relativity (without getting into proper time- see below). Firstly, there is the geometrical structure of spacetime given by the metric, but secondly
and for this thread more importantly there is the manner in which the global spacetime structure “evolves” in time. This doesn’t happen in the spacetimes of Galilean relativity, Newtonian mechanics, or the spacetime of special relativity, all of which have “static” spacetimes.
But even here, this “static” background spacetime isn’t enough to adequately express how, in modern relativistic physics, we actually use time as a parameter. Almost as soon as Einstein’s teacher reformulated his work from 1905 on special relativity into a geometric one a few years later, physicists developed another form of
time as a parameter generally called “proper time.”
This is because it is not that spacetime means (even as a mathematical model) that in modern physics we must treat space and time as one structure or “space.” As noted above, we can and could have done this with Newtonian mechanics. Indeed, what the layperson has in mind when thinking of “spacetime” is, thanks to popular physics presentations, somewhat closer to the spacetime of Newtonian mechanics or Galilean relativity.
In relativistic physics, we include a time dimension in the space (even when working with 2D spacetimes or 5D or whatever) because of the ways in which we require our equations of motion to be invariant under appropriate sets of transformations. Symmetries and invariants under transformations allow us to determine things like the group structures of the theory and therefore conservation laws (among many other important things).
And this leads to the final and perhaps most important issue with the claim: just because we formulate certain theories using particular geometries with particular dimensions and so forth
does not mean that we are making ontological claims. The metaphysics of spacetime is certainly interesting but it isn’t settled by the manner in which we (physicists) or other scientists use particular spaces, be they vector spaces or function spaces or complexified spaces or whatever.
In every sense of the word, in context of modern physics, you can't logically invoke "causality" to address the origins of the universe, as "causality" as we know it requires the universe to exist.
In the context of modern physics, we frequently invoke causality with radically different (often practically contradictory) meanings, including applied to universes which may exist at some future point or could have existed or which had yet to exist. Even in basic QM, the relative state interpretation still satisfies the causality constraints imposed by quantum theory yet also requires explanations for the causes of universes that do not yet exist. In standard cosmology, it is quite common to speak of causes independently of whether or not the universe (variously defined) existed. The basis for the flow of time is by some thought to be in some manner a cause of the initial conditions of our universe (or causally disconnected "pocket" thereof, or particular instance of a larger parameter space of possible universes), thereby essentially attributing the nature of time itself (which, intuitively, is something that causality requires) to initial conditions that had no such directionality. Much of this (IMO) is nonsense, but the point is that appeals to modern physics fail here, as you are getting into metaphysics at best and mostly ignoring actual physics literature and theory while doing so.