Even that ability is radically different and unique in the Chrono world. For Project Kid, he may have had the use of the Neo Epoch, the power of the greatest supercomputer ever built (which was on an island far from Belthasar in CT's 2300 A.D.), and most importantly, the Entity's aid (the extent of which is unknown).
Certainly, the use of the Neo-Epoch and "the greatest supercomputer ever built" are substantial benefits, but are they enough to explain the god-like implementation of Project Kid? I would propose that alone they do not.
1) The Neo Epoch: A terribly useful device; it could not only allow him to gather data to formulate his plan, but he could have also used it to nudge “history” in the right direction if it wasn’t heading towards his desired goal (has it ever been discussed if Belthasar might have been the one to cause the fall of Porre?) However, its use is limited by Belthasar’s own life span. He had 13000ish years worth of history to predict (could he even predict when Lavos might pull Chronopolis back?) and control; certainly he couldn’t have given his full attention to all those years (and all the people that there entails).
2) Fate: Of course, FATE is terribly useful for controlling factors for most of history; it prevented the citizens of El Nido from behaving in a way that would alter time beyond what Belthasar planned for. Unfortunate, that doesn’t apply to every other human in the world that could have been influenced by El Nido (consider Porre; Belthasar couldn’t rely on FATE to ensure that they behaved according to plan). As for FATE helping him plan, the computer had a "huge repository of historical knowledge dating back to prehistory," but as the existence of the civilization of Zeal was not known definitively by Chronopolis Scientists, this repository seems to have significant limitations. Even apart from this, the repository could not have contained complete information on contemporary times (recorded history just doesn’t contain the sort of information necessary to definitively predict counterfactual histories).
Without overarching principles, Belthasar planning Project Kid seems like an impossibility. There are too many variable that remain unknown (and unknowable) for Belthasar to construct a definite route to producing Serge as he is in the game. It would be akin to throwing a beach's worth of sand into the air in such a manner so that, when it fell, it would produce a perfect model of Edinburgh Castle. It is possible, but it is an undertaking that seems to be totally beyond the means available.
Yet I said “without overarching principles.” At first glance, Project Kid seems even more difficult than throwing sand to make Edinburg Castle; at least sand always falls down. Yet why shouldn’t there be laws governing the behavior of time, just as gravity governs the behavior of falling objects. Admittedly, assuming a natural "sixth sense" about how time works is probably too much, but Zeal was a highly advanced civilization and at least two of the Guru's worked extensively with time. It is not unreasonable to suppose that Zeal in general (and possibly just the Guru's in specific) were able to develop an understanding of 4th dimensional laws of physics; a framework for understanding how changes to the timeline will play out. This is actually supported by Gaspar, who was working on a device to restore lost timelines. Such careful manipulations of time would seemingly require substantial understanding about the mechanics behind the loss of those timelines in the first place. With enough experience working with such a level of temporal science, one might just as easily gain an intuitive knowledge of time (again, just like how a pool player can develop an intuitive understanding of how billiard balls will bounce off each other and the sides of the table).
With such a scientific background, Belthasar could have intuitively known (but still based on mathematical principles) that Crono and Co were headed on such a course through time as would result in the need for them to use a time egg (presumably, in this timeline he never built one of his own).
However that still wouldn't necessarily explain why he conceived of the poyozo before he met Crono (he references them, but it isn't certain that they existed at that point). Unless, that is, he knew that the que ball had been hit (and even if he didn't see that happen, he knew history well enough to know what balls it needed to hit in turn and thus was able to deduce where it would come from and where it would be heading). As you said, the Entity helped him in some ways (the extent of which is not known), so it may have been as simple as the Entity communicating in some manner that it had started a traveler down a path that could lead to the salvation of the future.
Anywho, just a
Thought