You're not going to get it much earlier.
Firstly, you need percussion caps, which are really only available in the 1830s or so. And early caps were tricky. Mercury fulminate can go up if jostled or dropped, and require really pure chemicals, but the reliability of caps has to be a lot greater if you have a hundred or more jostling in a hopperof a gatling gun than if you have a handful in padded cases, eg for a revolver.
Then you need cartridges. The earliest Gatling guns used paper cartriges, iirc, which were exceedingly unreliable. You really need drawn copper or brass cartridges or a machine gun, and the tech for that was only just arriving - at least for making thousands at once.
Then, you need the precision machining needed for breechloaders - and not just manual breechloaders, but automatic ones.
I doubt you could get a gatling gun equivalent functioning reliably in the field before 1850 or so. I really wanted to push that back to the '40s for my tl, and couldnt convince myself it was possible.