There are so many diverse directions that inventions and processes have gone its hard to see and choose any particular mechanical invention.
As one process is started it goes into the next, for example iron ore smelting/bronze/tin etc and then the refining of iron metals into steel and all its variations without which non of this 'Future' would have happened so fast.
The wheel is only part of it and its progression into the pneumatic tyre so beloved of us all now. To drive that tyre you need steel and gears, then an automotive drive, carbon fuel or electric.
this brings us to the petro chemical industry where oil and fuel are found but also coal is a fuel so we are back to the blast furnace.
I see it as a giant, 'Thread' picture with threads leading all over and interjoining into every process.
One aspect is the making of glass and the first windows, 'Bulls eye' glass where a glass balloon was blown and then pierced and spun into a sheet of glass with a dimple in the middle. But that was a progression of something else, not an invention but a process.
So what was the first invention ? the cleaved Flint to cut with or the pierced fish bone as a needle.
The band is so broad I doubt if any one thing is first ! As a simple native, all he needs is a spear and a bow and some arrows and something to cut with, modern man cannot survive without constant music and fags and alchohol and TV. The rest follows as a progression.
Clive