Most antenna manufacturers will supply you with measurement data of how much power is radiated in which direction. That is a perfectly normal thing to do, and it's much more likely you'll get one of these measurements that fully describe the far field of your antenna then measurements that suffice to do a simulation. For example, something like:
for both the E- and the H-Plane. Having two orthogonal cross-sections of the amount of power radiated in the respective angles fully describes your antenna's directivity. Nothing to simulate.
These are called radiation patterns. When buying non-trivial antennas for use cases where approximate knowledge of the directivity isn't enough, it's expected that the manufacturer has done the measurements necessary to generate them – it's practically impossible to do this at home, without an anechoic chamber and calibrated reference antennas.
You probably won't get exact fabrication data of what you can buy as patch antennas, but you can simply measure them with a ruler – so PCB type antennas should be OK, too, assuming the substrate is well-known (for cost reasons, and because at these frequencies it still works great, it'll be FR-4, anyway).
What you're describing is antenna simulation. Such simulations are usually rather complex finite element method simulations, that, by decomposing the antenna geometry and the time or frequency domain into small enough parts can mathematically approximate the antenna's fields well enough. You don't have to re-invent the wheel. There's software out there that does that.
As a free software, have a lookt at OpenEMS.
By the way, if you're really experienced, then your simulations are meaningful. I've rarely seen someone generate a simulation that is closer to measured reality than an educated guess at the first try.
So if your goal is to learn how to simulate antennas, start with very basic ones. A dipole, then a rectangular patch, then a patch with receded feedline etc, not with something as overwhelmingly complex to simulate as real-world 3D aperture antennas.
If your goal is to get a very good impression of what an antenna will behave like in usage before buying it, than the manufacturer's measurements are way more useful than a simulation.