I am not for positive
Do you mean the first one that was desigend to be used by the homeowner, such as a rental. Or the first one marketed and sold for home use?
The first rentals, at least in my area was the gigantic thermax type machines. Then later the Rug Doctor.
Home type, I believe was a Bissell, again I could be wrong; but I remember the old type that you hooked to the fawcett and pulled the machine along behind you. They had a big honking machine prior to the self-contained unit which I think the Big Green was their first self-contained.
I am open for correction.