Infinite regress is possible if beginning is singular. You just need to know a little about math to imagine this. Just think of a curve which tends to infinity at origin/beginning. Each segment along this curve could be a cause. So you have infinite set of causes in area close to origin which take short segment of time.

The Borde-Guth-Vilenkin theory has demonstrated that past spacetimes cannot be infinite for a spacetime like ours that is, on average, expanding. To quote their abstract, “inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.”

arxiv.org/pdf/gr-qc/0110012.pdf

I would also point to a little-discussed point that infinitely-expanding DeSitter spaces (e.g., empty spacetime with only zero-point energy) are not stable over infinite futures, at least according to current models.

I also think your argument runs into the quantum nature of reality. Eventually, you reach the Plank scale, and physics breaks down. Again, its the jumpy nature of a quantum vacuum, which is a product of the Uncertainty Principle, that prevents both truly zero energy from existing in the physical universe that prevents.

More generally, infinity is not a physical phenomenon that has ever been measured. An infinite future spacetime is entirely speculative.

This is the most important distinction. A theoretical infinity is imaginable, however a natural infinity is nonsensical.

I would also point out that the very notion of a physical curve is an assumption. Why would an initial state of the universe include a curve of any sort? A “curve” can also be described by a nonzero (or non-constant) first derivative. Why would dy/dx of any curve be nonconstant at time zero? Violates the law of conservation of information in physics.

Agreed. Go Blue.

The curve simply show the intensity in number of causes.