It's a little hard to decipher exactly what you're asking.

There were, of course, plenty of deadly weapons before firearms. Firearms, when first introduced, could be deadly, but they didn't dramatically change the battlefield. For example, the Chinese had fire lances before the Mongols, but the Mongol's other advantages (excellent military intelligence, highly responsive chain of command, etc) were sufficient that they decisively defeated the Jin and ultimately the Song (although the Mongols did incorporate guns into their forces (in a limited fashion) later).

Universally-feared, though? I don't know. Personally, I'd be scared of a mean guy with a baseball bat, but then there are people who are willing to strap themselves with explosives and detonate them on a bus. The Zulu impis, at least, seem to have regarded firearms as, at least, less scary than whatever awaited them if did not display proper discipline and obedience on the field of battle.

Generally, unfamiliar weapons could be unnerving to those encountering them for the first time. For example, Livy records in Ab urbe condita that Macedonians coming upon the aftermath of a skirmish between Roman and Macedonian cavalry scouts found it horrifying to see the wounds caused by the Spanish swords (gladius) the Romans were using, in comparison to the wounds caused by javelins, arrows, etc. It's notable, though, that the skirmish itself killed almost as many Romans (35, according to Livy) as Macedonians (40), so in spite of the shockingly graphic gore the gladius inflicted, it didn't provide some insurmountable advantage. Likewise, Anna Komnene seems to describe the late 11th century Frankish crossbow as a kind of superweapon in the Alexiad, but I think most modern analysts would say that its advantages over the sort of Turkish-style composite recurved infantry bow that the Byzantines themselves used, in trained hands, were circumstantial at best.

This question needs some unpacking. To start with "cannons/firearms" covers a very wide range of weapons, from pistols to massive bombards, from chinese arrow-throwers to assault rifles. A firearm is a weapon that throws some form of projectile by means of an explosive charge. What category should we compare to that? Are swords, axes and clubs the same category because they cause injury through leveraging the user's own strength?

We should also qualify what we mean by "universally" - literally across the whole world, or by everyone within a particular region? I'll talk mostly about Western Europe as I know the most about it.

As lot of other people have pointed out, the crossbow is a good comparison to the handgun. Early handguns had very similar characteristics to crossbows - they were both able to penetrate armour at short ranges, but slow to reload and vulnerable to cavalry if not protected by terrain, fortifications or pikes. They were used alongside one another for centuries. Heavily armoured knights continued to fight in Western Europe for centuries after the introduction of handguns.

When it came to sieges, cannons took over more swiftly from earlier artillery (although we're still talking a century or two). However it didn't take that long for fortress design to respond (the 'trace italienne' star fort) and siege durations returned to something like their earlier duration.

The use of firearms did not sweep across the world as a sudden revolution, it spread and developed over centuries. Remember that sabre-wielding cavalry were still a powerful force into the 19th century.

Perhaps the question to ask is 'is there another type of weapon that was ever so universally dominant?'

I think the answer to this is probably no - qualified by the fact that I'm not really sure what a comparable category would be. It took firearms the best part of a millennium to reach this position, but I don't think any combatant in a modern army is without a firearm (except for some cannon-less aircraft). Firearms also seem to be the most common personal weapon of choice except where regulated by law.

The closest comparison I can think of might be a horse in certain periods and places. What would a fighting force be on the steppe without horses? But even cavalry were marginal in some situations (eg. they were not decisive in Greek hoplite warfare) and useless in others (eg. naval combat).

(Main source: Bert S Hall, Weapons and Warfare in Renaissance Europe)