Tar is extremely old as both a natural material and a human-made material. Natural tar-like bitumen has existed for geological ages, while human-made birch tar belongs to very early prehistoric technology.
There are two different answers to this question. Natural tar-like materials, especially bitumen and asphalt seeps, are geological substances that formed over immense spans of time. They were available to ancient people long before written history. Human-made tar is different: it requires people to heat organic material in controlled conditions and collect the dark products that come out.
The oldest famous human-made tar is usually discussed in connection with birch tar. Archaeological finds show that prehistoric people used birch-bark tar as an adhesive long before agriculture, cities, or metalworking. It was used to fix stone tools to handles and may represent a surprisingly advanced understanding of heat, materials, and timing.
Wood tar as a major everyday material is much later in scale, even if the basic idea is ancient. Once boats, buildings, rope, carts, fencing, and tools became central to settled life and trade, tar became more important. In Scandinavia and northern Europe, wood tar production eventually developed into a serious rural and export industry.
So tar is old in several layers. Nature made tar-like substances first. Prehistoric people learned to make adhesive tars. Later societies turned tar into a strategic material for ships, ropes, roofs, roads, and industry.