I'd like to point based on my knowledge that the first Europeans to encounter China and Japan actually had rather positive notions. Francis Xavier, the Jesuit founder who went to Japan around 1549, wrote that the Japanese people were the "Best people yet discovered"; later Jesuit writers similarly praised them for their intelligence, amongst other things. Jesuits in China also generally admired Chinese culture and in some cases freely admitted Chinese/Japanese superiority over Europe in certain aspects.

To approach your question, then, I'm not sure when the stereotype of "smart Asians" came into play for modern times (I would suspect it's a reasonably recent phenomenon resulting from Asian immigrants in the USA), but I would posit that 1. Europeans who actually experienced/wrote about early cultural encounters between the East/West did not always view themselves as best and 2. A general strand of admiring Asian knowledge/intelligence/philosophies etc. has existed in the European discourse for a rather long time.