I am confused: Without contact to the AI one cannot even know which ones are in the game, even less if one (who does not have it at the start) researches Mysticism?
I believe that contact with the AI Civs is required for espionage tracking, since it requires cities to be revealed. Even a Spy or Great Spy revealing a city or even its culture would cause contact with the owner of the city. This could be considered a bug, if the Spy is not compromised such that its owner is revealed. A Great Spy can never be comprised and really should not cause contact with the AI, but the game does cause such AI contact.
Without contact with the AI, one can still learn about the AIs one is up against; in particular what the strongest in any demographic is and the weakest. One knows what units each AI starts with at a particular skill level and can look at the power demographic to deduce whether their are skirmishers; if so, one AI is known to be Mansa Musa. I believe their is also a demographic similar to score that will allow one to deduce with unique starting technologies they have such as Mysticism. Based on skill level Monarch to Deity, all AIs will have Archery (Monarch) to Archery, The Wheel, Agriculture and Hunting (Deity). So, the demographic will also reveal the starting technology of Fishing, but Fishing is cheaper than Mysticism, so those two unique starting technologies are distinguishable.
Of course, without contact with the AI, very little can be determined about them, beyond what I mentioned above. A little knowledge can be enough to predict how early an AI could build Stonehenge and thus aid in building Stonehenge oneself at the latest possible turn that should beat the AIs best possible date. The more information one has, the better one's AI Stongehenge date becomes, but that usually means contact with the AI and it's cities. Without contact with AI, very little about one's AI opponents can be determined, but it can be enough to make a ball park estimate of Stonehenge based on whether any of the AIs starts with Mysticism as revealed in the demographics.
If one tries to be a Sherlock Holmes, it is quite amazing what can be deduced from the demographics tab without any AI contact at turn 0, turn 1, turn 2, etc. You can track the various demographic values, make hypothesis and often either prove or disprove them as the game slowly moves forward turn by turn. Even spreadsheets and scripts can be applied to the demographics to reveal information that one thought was impossible to know. Such effort is probably not warranted in even competitive venues like SGOTM (some teams do it though), GOTM and HoF; it is definitely over kill for games played for pure enjoyment, unless one likes to solve "unsolveable problems".
To clarify, nearly everything I stated
prior to this post assumes contact with most or all AIs and the locations of their capital and other early cities capable of completing Stonehenge first. With such knowledge, one can track the build progress of each city (with no spies!) by taking the espionage needed to destroy progress on the current build for a particular AI city, multiply that value by 108, divide by the espionage needed to Support City Revolt in that city, resulting in the Hammers invested (rounding up to the nearest whole number). I have personally verified this computation dozens of times in many different cities and it exactly matches the value as revealed by World Builder or having enough espionage on the city to actually look inside the AI city directly in-game.