Let's try a different answer that plays not on what was invented during the period, but the advancements that the period brought to the world: Subtlety and magic's prerogative to keep the user alive are the two main reasons.
Disclaimer: I am going to base this on the premise that "discovery" for the purposes of this question means both the actual discovery of magic as an ability, actual proof that it is magic, and the somewhat widespread dissemination of that information. A painter can have a magical talent, but unless they are overtly using magic to paint, then it's just a man's claim.
Magic, until the First Magical Revolution, is just not about big flashy effects. It is subtle, and easily mistaken for chance, good genetics, or just having the gift.
Magic up until this point is the twice a decade prodigy in a trade, that child that can pick up a tool and just understand how to use it in the way they want to. It is the soldier that has survived a dozen battles through injury and infection to survive to old age despite the odds. It is the cunning thief that uses their "instinct" to avoid trouble from all sorts of people. It's the craftsman that creates something that lasts just a bit longer than it normally should. There is nothing that screams overt magic, but a myriad of coincidence and good fortune that is more than just good genes.
If you want to go that way, there are a blessed few that have figured out the secret of making magic flashy and powerful and truly bend nature to their will. We call those people "gods" and they form the basis of mythology.
Magic's first prerogative is to keep its user alive. When a person is sick or injured, it is magic that assists in the healing process. Whether it is disease, malnutrition, or injury, magic supplements the body until it is in peak condition, with or without magical help. As above, this is a subtle boost and not visibly fast healing. For those that lack the power, then their self-healing abilities can only go so far or fail outright when put under too much stress.
Since most magic is tied up keeping the body in prime (or just functional) shape, there is not the power to actually be flashy and powerful. And for those that have all their magic tied into their health, well they have the power, just apparently not the ability.
The Industrial Revolution
What does this have to do with the First Industrial Revolution? Technically nothing. In this case it is not any one invention, process, or discovery that will enable the widespread discovery of magic. It the other things that comes from this revolution that will enable the discovery of magic.
Better living conditions can lead to better health -- now magic that might have been tied into keeping people healthy is now free to be used and expressed. As such, there is more of a chance to be either blatantly flashy or actually observed and questioned
The lower infant mortality the revolution brings on allows more children to survive and awaken to the potential to be magical and for that magic to supplement the child's health. Also since they're healthier, they have more of a change to have free magic to use.
More organized science coming from a larger population and a boom in scientific progress can lead to discoveries that, while individuals dismissed single events, together they paint a trend of anomalies. Anomalies like magical phenomenon. New science and math may give symbols and non-instinctual understanding of magic allowing for collaborative discoveries where if there were any before, they were individual ones.
Just a higher population in both number and density can lead to just a higher chance that magic will be discovered and studied. As well as the mage not being killed on principal. While the probability is non-zero earlier, there are more chances now as opposed to then.
The enhanced understandings of the world leads to things that were once magic to be understood. Things that might have been written in antiquity as magic and wizardry are now science tricks. We have removed a critical mass of mundane magic and have definitively found the gems of real magic within.
Admittedly, none of these outright prevent magic from being discovered earlier. The idea is that while discover was a non-zero chance then, it is a much higher chance now.