Cannabis was smoked in different forms throughout the Middle East for probably centuries or even millennia prior to the Columbian Exchange. However, I don't know if the tradition ever took hold in any parts of Europe.

The word assassin comes from a group of 12th-century soldiers called the Hashshashin, which is indirectly derived from an Arabic term for hashish users. The term was apparently never applied to that group in the context of smoking hashish, and the link between these terms wasn't made clear until the 19th century. So it's unlikely that the introduction of the word assassin into European vocabularies suggests a knowledge of hashish at the time. Perhaps there was knowledge of hashish in Europe through other channels, but even if that were the case it doesn't seem to have ever taken hold.

Europeans definitely burned plenty of things for the purpose of creating smoke. Incenses come to mind, especially for use during religious ceremonies. But these were not "smoked" by any one person.

Tobacco was certainly being smoked by indigenous peoples of the Americas at the time of contact. If the concept of smoking was introduced to Europeans at any one time, this is the most likely scenario.

It is probably a stretch to say that smoking was "non existent" in Europe before tobacco. Keep in mind that some parts of Europe were Ottoman territories at the time of contact with the Americas. But whatever smoking, if any, occurred in Europe before then, it was probably very minimal. Definitely not to the point of permeating the cultural norms