What measurements do I start with for end result enlargement 43ft 4inches wide by 8ft 8 inches tall

If your design is entirely vector, size doesn't matter, prefer small size to ease the load on your device. Your artwork can be scaled up to any size without losing details. If you have rasters in your artwork, discuss this with the printer. For such a big canvas, they will have specific requirements. You should contact a person who is already doing this.

If this is a wall graphic that will be printed by a display vendor, have a chat with them as to what they require.

That being said, with murals I have done, I typically do the artwork quarter-size, so make your file 130" x 26". Give yourself at least 1/4" of bleed at that size (for a final bleed when enlarged of 1" which gives the vendor plenty to play with). If you work with images at 300ppi (i.e., export your final PDF at 300 ppi), these will drop down to a very respectable 75ppi when enlarged 400%. This is more than fine for a large graphic like this.