To get this done commercially, what you're looking for is any sort of light-engineering or metalworking facility that offers surface grinding.
Surface grinding is how very flat surfaces are achieved in many metalworking applications and it is how most or all planes have their soles flattened in the first place1.
As this is a modern mass-market plane (or low-end plane, depending on how uncharitable you want to be) it's unlikely you'll be able to find a service that will do this for a fee that makes sense — if done on the books, their minimum charge per hour could more than double the effective price of the plane (if bought new).
One other (cheaper) possibility that has been mentioned in some posts online is looking for a nearby high school that teaches metalwork, where the shop teacher might take on the project for fun/as a teaching example. But the almost complete disappearance of metalworking classes from American high schools (source: mrpete222/tubalcain) now makes this possibility remote.
And it's worth realising in advance that neither of the two options above would come with any sort of warranty. Without proper fixturing — clamping in place to prevent movement, as well as providing good support to prevent flexing — the grinding could be completed and the sole could still not be flat, in just the same way that rounds of sanding can be done and when the sole it checked it's found not to be much flatter than before.... or even worse.
machining service for handplanes
In addition, as this is a cheap plane spending much more than maybe the price of a coffee or two on flattening the sole doesn't seem to make economic sense. But there's good news below.
On another note I also read about someone flattening with a belt sander. Any reason not to try that?
If the platten is long enough and flat enough, you do it carefully, and you are suitably cautious of the sparks which can theoretically start a fire this is one of the ways one can speed up the process of flattening a plane sole (or working a cheek square to the sole2) in the modern workshop.
But.....
The sole doesn't need to be flat for the plane to work
As this is a jack plane, used for its original purpose — as a type of roughing plane (think of it as a big-ass scrub plane) — then the sole doesn't need to be particularly flat for it to work as needed.
Without getting into it too deeply, 5s are too long to be effective smoothers and much too short to be effective jointers3, so their original role is the only one that really makes sense.
So I would advise not chasing flatness on this plane and seeing how it works as-is once the iron has been sharpened with a suitable camber.
1 Obviously this plane should be very flat as a result, as the box promises. But it appears that most cheaper planes (and some that aren't cheap at all!) are ground when the rough castings haven't been allowed to 'season' properly..... no surprise, as reputedly this takes years to fully complete. When you don't wait long enough, after grinding some distortion can occur due to the cast iron still settling down.
2 Note that this is not actually necessary. Including if the plane is used for shooting!
3 Even 6s at ~18" long are generally considered a little short for this (you want at least an additional 4").
