Can we speak of an absolute voltage without a convention? In most practical cases I have seen, voltage was regarded as a difference in electric potential, save the odd change of magnetic flux over time which, as a form of change, also conveys the notion of a difference.
However, from what I gather, we can ask ourselves what a sensible basal level for an electric potential might be (for example, the potential an infinite distance away from the electric charge producing it) and treat any voltage expressed in relation to it as an absolute voltage. But then we need to agree that the potential at infinity is zero. I do not know whether there are other sensible choices, but I am willing to accept that there might be.
My question is whether there are any other senses, not involving a prior agreement on a reference value, in which we could speak of an absolute voltage and, if there are, what senses would those be?
 A: You are asking if there is a natural sense of “zero voltage” in some contexts, regardless of prior social consensus. And you have already identified one example, that if you have a confined set of charges in 3D then it is quite natural with the $1/r^2$ force law and $1/r$ potential to interpret infinity as zero voltage.
To this we can add some other examples: if one is attempting to do electromagnetism in 1D then the force becomes constant with distance and it makes sense that $U = k~x$ for some $k.$ This may seem artificial because we are located in 3D space, not 1D, but it corresponds to a 3D infinite plane of uniform charge, which can be used to describe what things would look like if one were shrunk down and found one's self inside a parallel-plate capacitor, or so. The natural zero of potential due to an infinite plane of charge, would be located on that very plane.
Similarly if one is thinking about a point charge next to an infinite conductor, the fact that an infinite conductor must be at constant voltage leads to a natural desire to set this voltage equal to zero. One can then fully enforce this using the method of image charges.
Conversely sometimes there is no natural zero. In 2D rather than 3D, one finds a $1/r$ force law, which must admit a potential $U_0~\ln(r/r_0)$ and this cannot be normalized to be zero at infinity or at the place where the charge is located. This corresponds to a geometry of a charged infinite wire, and one just has to arbitrarily choose a distance $r_0$ away from the infinite wire where the potential will be zero. There is no “natural” preference for one choice versus another.
I can also read you as asking if such “naturalness” things are always social conventions, if naturality is just a matter of physicists’ habit. That is a much harder question. In the specific case of 3D, you can regard infinity as a sort of boundary condition, and the choice to make the potential zero there has more of a rigid mathematical justification: it makes the solutions additive.
The problem is that you could always override it, you can always choose a different convention and say that it makes no physical difference. So for example we could have absolute voltage if only I could describe to you a process by which I will insert some electrons into the voltages that you describe, and we will measure the energy required. This seems very natural, but then you look deeper into it and realize that we are actually just agreeing on the voltage of my secret electron source, we are agreeing that that is zero, but maybe you prefer it to be +12V or whatever whatever. I am inclined to think that there is still a natural reason to choose these things over other things, but it is correct to say that the Maxwell Equations cannot predict anything differently no matter which reference you choose.
A: Voltage is a measure of potential energy, and can only have a particular value at a point if you choose another point as a reference where the potential is selected.
A: The best you can do in an experiment is to surround the experiment with a Faraday cage. Then, the natural choice of zero potential for the experiment is the potential of the cage. However, the cage itself may exhibit a nonzero potential as measured from outside.
This is more common than you might think, because usually there's a lot of stuff around at similar potential (conventionally termed "ground potential"), so you're working in a mediocre Faraday cage.
