There are several ways to go about it, but here’s one way. I’d create a Photoshop file at that aspect ratio. Then I’d copy and paste the Illustrator paths into Photoshop as a smart object. I’d scale the smart object to fit, then rasterize the layer and flatten the file.
Illustrator crops to the art on an artboard unless you tell it not to.
When you Export > Export As
Select your jpg option then check the small box at the bottom of the dialog box that says “use artboards”
It’s rare that I create in Illustrator when a raster image is the deliverable, but in such cases, IlIlustrator’s image export has failed me in one way or another pretty much every time. Get it into Photoshop, from which a proper raster image can simply be written via Save As or Save For Web.