dS space is really simple; you only need a cosmological constant to power a uniform metric expansion, and no matter to retard it. The far future dS space approximation has only localized matter, namely mostly isolated gas molecules and (swarms of) black holes, each occupying their own Hubble volume, as all their non-gravitationally-bound neighbours have disappeared across the horizon.
Unless something really unexpected arises to retard the metric expansion of space -- and many working scientists are looking for that, since it would be amazingly cool -- that we see right back to the surface of last scattering, the "in theory" part looks very sound.
"If I cannot create it, I do not understand" -- well, get yourself a very fine spectroscope and a monochromatic radiator (or an ideal blackbody, or anything with a highly predictable emissions and/or absorption spectrum) and probe the infinitesimals in the Poincaré group, which is the isometry group of Special Relativity (and which, incidentally, is what fundamentally defines Minkowski spacetime). https://www.wikiwand.com/en/Modern_searches_for_Lorentz_viol...
An experiment or observation inconsistent with infinitesimals, or preventing the far future dS state implied by observed energy-densities, would be groundbreaking.
Although your objection to a physical infinity, or physical infinitesimals as their complement, are aesthetic ones that conflict with experiment to date, don't let that stop you from thinking about, or even proposing, novel, objective, and repeatable experiments that probe the abolition of real numbers.
Just today Baez just helped you out a bit: https://arxiv.org/abs/1609.01421