It helps to be mechanically inclined. But its also profoundly important to have actually used your hands... in multiple disciplines, arts, and trades.
Born a Designer
The first thing I ever designed was a log cabin. I think I was two years old? However, I was quite frustrated that there were not enough parts in your typical Lincoln Logs kit.
The first thing I remember drawing was a car. It had five V8 engines and the body of a shark and it could eat other cars.
I remember having trouble designing the gears that meshed the drive line to the rear axle as I hadn't got a peek inside a differential yet. I think I was two then as well.
I didn't play with toys; I broke them apart to see how they worked. So my parents switched to Lincoln Logs, Tinker Toys, Legos, Erector sets, electronic labs, chemistry labs and such. Mom actually had dad install a secure steel cabinet in the garage as a safety factor for my chemistry stuff. In 6th grade, I built my own shed (to code) in the back yard, complete with solar collector, to hold my tools, workbenches, supplies and projects. In High School, my bedroom looked like an electronics laboratory.
Dad took me on is construction and remodeling jobs. We also installed a ton of metal patio covers on trailers. My sister taught me how to replace brake pads, after dad taught her. We rebuilt engines, created custom train sets and did all sorts of crafts. Mom taught me the sciences behind cooking, painting, sewing and interior decorating.
I have designed (and built) music equipment cabinets I took through airports, a jib (crane) to take my camera from ground level to 50 feet in the air, and I've designed labels and packaging for beer bottles used in my movie. I've designed and built workbenches, ventilation systems, and storage cabinets for my employers. I've designed, installed and maintained entire computer, data center and phone networks and infrastructures from the ground up.
Its not that I can design just about anything, but that I can pull from multiple disciplines, arts, and trades.