1870's-1880's Europe or America maybe for heavier than air flight, but you'd still need to be in a technology center to borrow from a lot of existing knowledge, manufacturing capacities, and a development team (something that the pioneer aviators mostly lacked,operating in relative isolation and far from such centers.) Maybe it's a ship-building center like Glasgow, Bremerhaven, Liverpool, Norfolk, etc. with the ship's propellers technology emerging in the 1850's pointing the way for aircraft after 20+ years of development and use. The British Navy had the most advanced steelmaking processes (secret) in this era and the Royal Society was doing the most in cross-fertilizing science at the time, so maybe England makes the most sense (including expertise in steam engines but proximate enough to the continent to be aware of Otto Benz and Rudolf Diesel work in Germany on engines.)
Kerosene refining is already well underway (U.S. from 1869 Titusville, Pennsylvania not sure where and when in Europe whether it's Przemyl, Ploesti, or elsewhere) while whale oil would be the light lubricating oil for the engine or potentially the fuel. Diesel engines originally ran on vegetable oil, so you're just crushing oilseeds (soybeans, corn, olives, sunflowers, hemp, rapeseed, nuts, etc.) so the fuel production would be the simplest by far there. Electrical components of all kinds would be a significant limiting factor given bulk, primitiveness, sparking/fire risk, battery technology, etc. which'd really limit utility and instrumentation longer than in OTL where they roughly converged.
Machining is considerably advanced by the 1870's-1890's in the U.S. (actually the world leader for precision-machining at this point), England, Germany, France, Czechs, Belgium, etc.) as universal milling machines, complex lathes, interchangeable parts, etc. are increasingly available and hand-filing gets them to 1/1,000ths of an inch which is quite a bit better than early car engines had (ask Henry Leland at Cadillac about that.)
Pistons, gearing, turbines, electrical batteries, mechanical and pressure controls, are all under development from railroad locomotives, steam engines, ships, clockmaking, typewriters, sewing machines etc., for that matter Alcoa has started making aluminum (1860's breakthrough) in Pittsburgh around this time which would have some interesting implications for engine components (casting and forging being pretty advanced by then) or airframe components.
Complex systems generally move a lot faster with lots of existing technologies and capacity to borrow and learn from, while they go really slowly if at all when you have to figure out and then make everything needed at one remote site with a small crew, limited funds, and endless learning curves.
Doing it in the 1890's seems quite feasible (MIT already offered a degree in aeronautical engineering by then which surprised the heck out of me) and 1880's maybe with the right development team drawn from some of the best minds of the time (and probably national government funding or the classic deus ex machina of a bored rich guy.)
