I'm not sure about the idea that a part of history can be so old that we cannot get information about anything older. I'm not sure if you mean history or prehistory. Now depending on your definition of what constitutes history, it begins about 5000 years ago with the first writing systems. So by systems I'm discounting things like painting on walls, as this cannot be used to transmit precise information about any topic within a language.

History only takes us to about the late 4th millennium BCE, then we must rely on archaeology for anything earlier. So history is limited in what it can tell us in terms of the scope of human existence. So there are a hell of lot of other things we could know that history can't and won't ever tell us. But we have a got a decent but far from complete understanding about how things developed from studying prehistory through archaeology. If you meant before human existence and beyond, then obviously that it outside the realm of archaeology. However, if you did indeed mean history, then it's also hard to give a definitive answer. Some little piece of history may show up tomorrow that blows us out of the water. As to religious interpretation, I'll leave that well alone.

Anyway, I'll try to answer your question in terms of the earliest pieces of history that are currently known. The earliest writing occurs in Egypt and Mesopotamia about 3000 BCE. Early Mesopotamian writing developed out of the recording of business transactions. So a symbol of a sheep might be inscribed on a token, which represented one sheep. Eventually these symbols became more abstract and turned into pictographs that could represent objects or ideas. Eventually, the tokens were discarded and the marks were instead written on soft clay and then dried into tablets. A sharp stylus was replaced with a wedge (which made them look even less like what they originally depicted), the phonetic components were added, and we get the first cuneiform writing in the early 3rd millennium in Sumer. So the first and oldest historical material was mostly that of business transactions, used to record the complex trade in Sumerian cities (Bottero, Mesopotamia: writing, reasoning and the gods).

These early writings eventually became full-fledged, literary tools. But early on they recorded things like king lists, such as the Sumerian king lists or the royal annals in the Egyptian Palermo Stone. In Egypt, the Palermo Stone lists names of kings that go into 'prehistory'. Some, particularly the Lower Egyptian (Delta) kings may even be legendary or fictitious. At the moment, it's difficult to confirm they even exist (Wilkinson, Royal Annals of Ancient Egypt: The Palermo Stone and its Associated Fragments).

Early Egyptian writing can be seen developing through pictographic representations in art and pottery that would eventually form hieroglyphs (Arnett, The predynastic origin of Egyptian hieroglyphs). Originally, the Egyptians developed pictures, which became somewhat standardised, that represented real world objects. However, eventually these would be used for a rebus effect, whereby combining symbol of an unrelated more abstract concept might be used to represent ideas with corresponding sounds. For example, in English, a picture of a 'bee' next to a 'leaf' could be used to mean 'belief'. The earliest history in Egypt would be the earliest 'rebus' use of hieroglyphs in this way, such as in the Narmer Palette, where the catfish hieroglyph (nar) and the chisel hieroglyph (mr/ab) combine to create an idea (the name of a king 'Narmer') unrelated to those two concepts. Though that being said, Wilkinson has made an interesting argument for the idea of a catfish as a power animal, connected to early ideas of kingship, so it may not be entirely unrelated (Wilkinson, What King is that? Narmer and and the concept of the ruler). I also note that some recent discoveries at Ouadi 'Ameyra in the Sinai desert point to the confirmation of Egyptian king, Iry-Hor (ca 3150 BCE), as being the first known person in history. The writing of this king's name, a 'Horus-falcon' hieroglyph holding a 'mouth' hieroglyph, was recently found with a serekh, an indicator of kingship (Tallet and Laisney - Iry-Hor et Narmer au Sud-Sinaï).

So these are the earliest known bits of history. But the are not so old that they do not preclude the existence of older information. For that you may have to look to archaeology, however. I hope answered your question adequately.

If, by the phrase 'recorded history', you're asking about the oldest-known document, that would be the Kushim tablet from about 3200 BC, which reads,

29,086 measures [of] barley [were delivered over] 37 months, [signed] Kushim.

Ergo the oldest recorded part of history is an accountant's record of a grain shipment.

If, however, by the phrase 'recorded history', you mean the oldest historical event which was written down by someone who might know something about it, and for which an exact date is known, then the answer would be the Battle of Meggido as recorded by the Egyptians. This occurred on what we would now call April 16, 1457 BC.

If you just want the oldest recorded event we know of from recorded history, but don't care if we can't pin down the date, then that would be... well, Kushim's grain shipment, probably.

Are you talking about a piece of writing or documentation? I think there are clay and stone tablets in Babylonia from 3,000 BC.

Gobekli Tepe is the oldest piece of architecture and religion. It dates to around 10,000 BC. With art you have the Lascaux Cave Paintings. They are from over 30,000 years ago.