In the absence of an actual expert on pre-medieval Scotland chiming in, I can provide a (short) answer as an historian who worked in Edinburgh for a long time, and had some natural interest in the history of the castle.

I believe the claim relates to the history of the castle fortifications, which are (contrary to popular belief) generally not medieval in origin, with the medieval elements of the castle being largely destroyed in a siege in the 16th century. What remains today is the post-siege reconstruction, which I believe is mostly of 16th-17th century origin when it comes to the fortifications, with new barracks buildings built into the 19th century. When the Scottish national war memorial was built after the First World War, its main patron, the Duke of Atholl, was frequently known to gripe about the objections he received about the prospect of any existing buildings being demolished to make way for the memorial, as he regarded the 19th century additions as having nothing to do with the castle itself, but were already by the 1920s popularly seen as part of its historic fabric.

In any case, the sign claiming that a different gate (or gates) defended the castle before the current fortifications were built is not controversial. But there is little certainty about when exactly the earliest fortifications were built on the site. I believe there is solid evidence for a fortified site dating to the first century AD - i.e. roughly 1500 years before the current gate - but while it has been argued that there was a settlement dating back to the Bronze Age, to my understanding this has never been definitively proven. I am very much not an archaeologist, however, and would gladly defer to anyone better able to evaluate those debates. To my mind, the sign shows undue certainty about the precise date, but it isn't completely made up out of thin air.