I'll admit, in my head, I imagine that Haki was "invented" slightly after after Devil Fruits were. But, there's no real reason for that, other than it reflects how they were introduced in the manga. Devil Fruits showed up first in the story, then we found out about Haki a long time after that, so I suppose the in-world history could follow suit. But, it doesn't have to.
They both probably came around about the same time, thousands of years ago, if not longer. Devil Fruits, Haki, and potentially "Symbol Magic" possibly all come from the same source. Likely, there's something that unites all these different power systems together at their core. It's possible that the Mother Flame or Forbidden Sun is the common source for all of these different power systems. One, original power that was split into "pieces" during a conflict of some kind. The Mother Flame/Forbidden Sun probably existed at the core of this World since the planet was formed. But, once it was "mined" in the First World, the power was altered from whatever it originally was. The Original Power System may have been something like Nika's power, the power to make anything you think of into reality. Pure "Dream Energy" of some sort. But, once it was "broken", the other power systems became more limited in different ways.
It's worth pointing out that all the major power systems respond to different "emotions". Devil Fruits are created by people's dreams, by imagining what the future could be like, the power of their souls. Haki is formed from people's willpower, the effort needed to change the present, the power of their bodies. And "Symbol Magic" seems like it could be from people's knowledge, their understanding of the past, and the power of their minds. So, in theory, the Original Power System would have responded to ANY emotion, not just a specific one.
Did these systems always exist? I...don't think they did. Not in their current forms, anyway. If Devil Fruits were created by technology, it's possible the other power systems were also somehow artificially created by technology. We know this World has been artificially altered in the past. The Red Line doesn't seem natural given that all the whales hate it, the entire Grand Line was potentially pulled into it's current position by Island Pullers like Oars, and we now know that the current "God" of this world can seemingly alter things to their liking to a extent. This world could have been heavily changed from what it was originally. Possibly after the Mother Flame/Forbidden Sun was "shattered". These systems probably all arose after the end of the First World.
Devil Fruits are a type of bio-tech, artificially grown by manipulating DNA and Lineage Factors. Haki could be some sort of nano-technology that covers everything on the planet, responding to "orders" from strong willed individuals, creating a steel-like coating around them if they "command" the technology around them hard enough. "Symbol Magic" could be some sort of world-wide "operating system", with the symbols basically being complex formulas or computer programs being written to control the environment, a way to literally "hack" reality around them by manipulating energy. It really depends on how much Oda's going to end up leaning into the potential sci-fi origins of this world.
As for who used them first? Well, it seems like the Forest God likely had a hand in making the first Devil Fruits. So, it would kind of make sense if the other Gods "invented" the other power systems. I feel like the Sea God may have had some hand in the creation of "Symbol Magic", given the power of the Abyss. Joyboy/Nika would kind of make sense for Haki, or maybe the Earth God, alternatively. But, if that was the case, that leaves us with a odd problem. If all the Gods have their own power systems...we should actually have FOUR power systems in this story, to go along with the 4 Gods. And we don't even really have confirmation that "Symbol Magic" is our major third system, yet. I suppose "Love" could be our Fourth Power System, but that's always felt more like a sub-system of Haki, to me, personally. I guess "Swords" could be another Power System? But, that feels like something for a potential missing Fifth God, if we go with the idea that the Gods are based around the Five Elements. I feel like "Love" would still be our best bet for another power system, possibly originating with Joyboy/Nika. Or some variation thereof, like "teamwork" or "sharing" or "empowerment". A way to pool power from several weaker people together, in order to make everyone stronger, perhaps?
Which does raise a question about what "Swords" could be in the One Piece World? Because, given all the background information we get about Named Blades, and the importance of "swordsmanship" in this story, Swords are probably...something important. We know objects can "eat" Devil Fruits, so Swords can use Devil Fruits. We know Swords can become Black Blades, which has something to do with Haki. In theory, Swords could be imbued with "Symbol Magic", as long as you put the right magic symbol on them. And if there are nanobots everywhere in this world, which helped terraform this planet in different ways in the ancient past, it's possible that Swords could literally be made out of semi-sentient nanobots, explaining how they can have "personalities" of their own. It's worth noting that most the objects that we've seen that have "eaten" Devil Fruits have been made out of metal. All except Smiley the poison gas axolotl, but it's worth noting that Hydrogen Sulfide DOES react with metal and can become a metallic conductor of electricity. So "Swords" would basically be..."robots"? Completely artificial people who can still do everything that regular humans can? Another "hidden" race in this World, that needs to be brought into society and get respect from the organic races? I dunno. This part isn't fully cooked.
https://onepiece.fandom.com/wiki/Category:Inanimate_Zoan_Users
https://onepiece.fandom.com/wiki/H2S
https://en.wikipedia.org/wiki/Hydrogen_sulfide
More thoughts along these lines over here:
https://worstgen.alwaysdata.net/forum/threads/will-eos-zoro-and-sanji-be-the-“sword-god”-and-“love-god”.77479/page-2#post-6529169
https://worstgen.alwaysdata.net/for...why-it-is-not-a-new-power.71689/#post-6289904
So, to sum up, I don't think Haki, or any of the current power systems, have existed forever. A lot of these were probably all part of the Original Power System that came from the Mother Flame/Forbidden Sun, until it was broken, and the power systems we have today all come from that original source. The 4 Gods likely had some hand in making these other power systems that we see in the present day. And it's possible all these power systems are actually advanced ancient technology, rather than anything truly supernatural.
But...I could be very, VERY wrong about all this. Oda could go any number of ways with this. We know so little about some of the deeper mysteries of this World. And I'm not really sure how much Oda will actually cover? Oda may keep a lot of this mysterious. Only covering the stuff that's more relevant to the plot in the present day. I hope not, but he could. Time will tell.