When in doubt about... a lot of general FFVII terms, your best resource is the
CC Keyword Collection; it's very diverse in the topics covered and there's a lot about the effects of both mako and Jenova on beings (and more importantly, why they work that way in-universe).
There's some pretty fun stuff going on there in the topic of "monsters".
Monsters
Living things, both plants and animals, who have been over-exposed to mako and thus suddenly mutated. The two causes are roughly divided between beings affected by natural springs of mako that well up from the soil, and those that were produced through Shin-Ra experiments. Therefore, in areas where there is little natural mako monsters are only seen on occasion, and as for the ones born from Shin-Ra experiments, many have escaped over the course of the war and have begun breeding in the wild.
Monster Investigation Program
A program aimed at gathering information about the appearance of monsters all over the world. As it is necessary to make contact with the monsters, this dangerous investigation is assigned as part of a SOLDIER’s duty. After investigating the monsters within Midgar, harsher missions have operatives traveling to uninhabited areas and islands.
Mako Humans (a.k.a. Makonoids)
Humans who have been continually injected with mako, and have turned into monsters. In addition to those who were being cultivated in the mako capsules in the Nibel mako reactor, there are also those in created by the research of Genesis’ group in the Banora underground.
So... monsters have always been around, in particular in areas rich in mako where it bubbles out of the ground natturally (Nibelehim, Northern Crater, Mideel). However, Shinra has been playing around with creating monsters via mako exposure and enough of those have escaped to start breeding in the wild as well. Shinra is itself aware of this problem and has an entire program that is... essentially making bestiary of what monsters exist where and that program is dangerous enough that it's SOLDIER that does that. The Makonoids in particular are human experiments exposed to mako... but even then it notes that they have to be continually injected with mako for that to happen.
So yeah, there's plenty of in-universe evidence that monsters would have been an issue without any Jenova exposure. It's just that since Shinra started experimenting with mako, there's been more more monsters in places that otherwise might not have had any of them. But monsters didn't not exist in the world either... they were simply more common in places with mako.
It's also worth pointing out that in order for "monsters" to be a thing, there had to be some other living thing around to get mako exposure and... normal animals can be pretty dangerous to people all on their own. Mako just... would have made them even more dangerous then they already were. Take something like a crocodile, lion, elephant, buffalo, komodo dragon, bear, etc. Anything people IRL know is huge and dangerous and then... have it hang around an area rich in mako for a while. Biologists must have always had a field day in the FFVII world when it came to taxonomy.
The ironic thing is... mako itself is a source of life. There is good reason for... just about anything in the FFVII world to want to live in a mako rich area as that is where life is the most... lush. Or rather, areas that don't have a lot of life aren't near mako. "Monsters" just seem to be what happens when something gets "too much" spirit energy. Although "too much" spirit energy varies on what the plot wants to happen at the time. However,
most reactions we see beings have to mako aren't from the first time they come in contact with mako. It's usually only from a lot of long continued exposure to it. So that is probably why not everything in a mako-rich area turns into mosters just from being in the area (the people in Nibelehim and Mideel get a lot more continued exposure than most people do and are fine). They'd actually need to go and... sit... in mako for long periods of time.
