Nobody knows who built the first jumpgates, but the current gate network is a modern invention.
The Vorlon building the Thirdspace artifact and having similar vortexes to jumpgate tech doesn't really hold up against anything. There are dozens of races just visiting B5 that use very similar technology to create very similar vortexes, and it is unlikely that any one of them created jumpgates. The Vorlon do have the advantage of being old enough to do it - but so do an unknown number of First One races. Current methods of entering and exiting hyperspace among those races may look different - but even among Vorlon and Shadows, tech progresses and is advanced, and we don't know if that's the way they always did it.
Gate design doesn't even really shed much light on the originators to begin with. We know from The Long Dark that jumpgates are like any other piece of machinery - they wear out, break down, or otherwise need to be repaired or replaced. So there's no telling if modern jumpgates operate in the same way that ancient gates do, or whether we can tell anything from vortex similarity. We do see occasionally different gate designs (there's a 3-rail gate in operation near Z'ha'dum, as opposed to the 4-rail design most often seen), but we can't say for sure whether those are recent or ancient constructions.
There is one gate in the expanded materials (Armies of Light and Dark from the Legions of Fire trilogy) with a confirmed 1,000 year old construction date minimum, built by Shadows and later buried on a dead world. At most it confirms special cases are possible, as the gate creates a point-to-point wormhole-type course through hyperspace to another gate. Whether it operates normally otherwise cannot be said, as it is only described open while still planetbound, and from the view of characters on the ground mostly looks like a vaccum-sucking dark hole straight to hell. It's destroyed shortly after.
So between average wear and tear, the sheer size of the possibility pool, and the lack of any good archeological examples, we don't know who first built jumpgates at this point.
Keying off of @Gaultheria's wiki link, I dug into To Dream in the City of Sorrows, one of the tie-in novels that's been stated to be mostly canon. It follows Sinclair and related characters after he leaves Babylon 5. While describing one of Catherine Sakai's exploration missions, the text diverges into a long infodump on the origins of an ancient jumpgate system.
She would be exiting hyperspace into normal space through one of the oldest jump gates ever found. Universal Terraform had estimated it at some six thousand years old. Though all the original jump gates had been built to last for millennia, they could be quirky and unpredictable in operation and she was poised to be the first Human ever to go through this particular one.
Nobody knew anything about the alien species who had built the original network of jump gates other than what the gates themselves revealed. The aliens had been highly advanced, and were extraordinary engineers. They had built the first gates maybe as early as seven thousand years before, and had apparently flourished as an interstellar civilization for some four to five thousand years after that – then vanished, leaving only their gates behind. No trace of their civilization beyond the gates had ever been found.
It continues on in that vein for a bit - to sum up, various races tried to explore the ancient gate network, but the original gates had no beacons so most of those ships were lost. This heralded the modern gate network as the original gates were reverse-engineered, replacements were made, and the beacon system established to allow safe transit. Humanity became spaceworthy right around the same time (the Centauri were looking for suckers... er, customers for their part of the network). Old gates, as shown, are still occasionally found and added on, but no one ever mapped the whole thing.
This does not explicitly rule out the Vorlon, but presumably what archaeology has been done on the ancient jumpgates would be able to match the tech to what little is known of Vorlon society, and nothing of the sort is shown.