If the size of the pyramid is a little bit "elastic", its age is apparently still more variable! In this article (en) (see "The figures really don’t add up"), Alun Salt picks up Mr. Osmanagic’s numerous contradictions: once he claims that the Bosnian pyramid has been made after the Egyptian and Mexican ones, the other time that it was constructed a long time before them (it is said to be "the mother of all pyramids"). The claims emanating from members of the Foundation are much varying on this subject: usually, the few scientists of the team are very discreet, and say they cannot make their mind until the excavations are much more advanced; while Mr. Osmanagic gives numerous peremptory assertions - and contradictory ones. However, the figure that he most often cites, as lowest or highest limit, is 12,000 years.
The scientists’ discretion is more than justified in the present state of things! The dating of a monument, during excavations, can be made using:
historical documents (for Antiquity): as fas as Bosnian "pyramids" are concerned, there aren’t any mention of them in whatsoever document;
stratigraphy, that is the very precise studying of the different layers that are on the object or around it: in the present case, according to the high number of photographs of the excavation site that can be seen on the official website or the forums, it doesn’t seem that there is a very careful study of the stratification; the upper layers of soil, which are covering the "pyramid blocks", are simply taken off, with spades or even bulldozers (see this text about the excavations);
the global study of the site and its surrounding: other artifacts, remains of dwellings, refuse dumps and so on; these elements are usually abundants, especially in the case of a monumental building where the construction must have lasted tens of years. In the case of Visocica, till now, no such element has been found.
the study of the civilization which made the site, and of its other achievements (comparison of the techniques used and so on); again, this method cannot be used here, as the supposed "pyramids" cannot be linked with any known civilization.
So it is not surprising that the few archaeologists present on the excavation site do not make any hypothesis for the age of the pyramids (and in fact do not confirm the pyramid hypothesis itself); however it is not the same with Mr. Osmanagic. In fact, the last obviously had a preconceived idea of their age, as, even before any excavation or study took place, as soon as he had his "revelation", he already gave hints as to their age: the pyramid of the Sun was built at least "at the end of the last glacial age" (in his book "Bosanska piramida sunca" (bs)), the only evidence given being the depth of soil (2,5 m or more, according to Mr. Osmanagic) covering the "pyramid" . "End of the glacial age", that is about 12,000 years, and this figure indeed frequently appears in Mr. Osmanagic’s claims, a figure that is not deduced from any scientific study, but from a "first impression".
Of course, this age for the "pyramids" raises some difficult problems: 12,000 years is still the Upper Paleolithic (Magdalenian); every known culture in Europe at this time belongs to nomadic hunters and gatherers, who definitely cannot be the builders of the supposed pyramids. Not for lack of intellectual abilities, but because:
of a lack of technology, particularly a lack of metallic tools (the first metals appeared much later, the copper about 6,000 years ago and the bronze 4,500 years ago)
and especially their economic system, based on hunting and gathering, was unabled to release the quantity of labour necessary to this type of monumental work. The men, during Paleolithic, are often barely able to survive, there are no food surpluses able to nourish an "unproductive" labour. Of course they are able to find time for intense intellectual and artistic activities (see Lascaux!), but here it would be a matter of hundreds and thousands people needed for the cutting and transport of blocks of several tens of tons (according to the estimation made by the Foundation for some "slabs" on the pyramid of the Sun). Monumental architecture does not and cannot appear before the Neolithic, when agriculture provides the food surpluses that will allow the existence of cities, and the possibility for part of the population of devoting themselves to non alimentary tasks - as is the building of a pyramid (see on that subject this excellent post (en) by Katherine Reece). The oldest prehistoric building in Europe, Silbury Hill (en), is about 4,500 years old, that is during the Neolithic.
So it is easy to understand why archaeologists do not easily take with serious Mr. Osmanagic’s assumptions. But how does this one justify the shift between the figure he claims and the common knowledge of Europe prehistory? The key is in his books: the pyramid would have been built by a mysterious civilization, extremely advanced, obviously directly connected to other mysterious civilizations, among which the Atlanteans’ one. The age of 12,000 years is obviously linked with this Atlantean civilization (see for instance the occurence of this 12,000 figure in the page "Civilizations before the beginning of official history" (bs)). What happened 12000 years ago, that would explain it? One can learn on this page (bs) that it is the time when happened a "cosmic cataclysm" (responsible for the disappearance of the Atlanteans), and that the rise "by several hundred meters" of the sea level that took place in Europe at that time has wiped every trace of this "super civilization" which created the pyramids. How convenient, to explain the lack of remains (beside the "pyramids" themselves) of this civilization...
 It must be noticed that it is impossible to deduce the age of an archaeological site from the depth of soil above it; this depth depends on various factors, geological (nature of the rock layers), topographic (site located on top of the slope, or on the contrary in the bottom), and especially climatic. For instance in the Paris Basin one can find Gallo-Roman sites hidden under ten meters of silts; on the contrary, in desert climate sedimentation can be almost null.