In order to produce nanotubes on this scale, two things must happen:
- They must be identifiable
- They must be engineerable en masse
- Henrich Hertz suggested in the late 1800s that electrons could travel in waves. This was important, because electron microscopy is the way we see nanotubes.
- Emil Wiechert then successfully used these waves in 1899 to produce a primitive first step to the electron microscope.
- Hans Busch showed that electrons could be used just like light to observe structures in 1926, but it seems that there was no factor short of interest and research funding that prevented this from happening closer to Wiechert's discovery; we could have gotten here sooner.
- We reached a resolution of 50 nanometers in 1933 with Ernst Ruska's prototype, but nanotubes typically have a resolution of 10 to 20 nm. This is a big difference to make up, but not monumental - it was mostly based on the much earlier research, so you could potentially push the date back if people had more interest. That would allow us to see nanotubes much earlier - but you can decide exactly where to get the research funding from.
According to a source linked below:
CNTs have probably been around for a lot longer than was first realized, and may have been made during various carbon combustion and vapor deposition processes, but electron microscopy at that time was not advanced enough to distinguish them from other forms of carbon
Well we've taken care of electron microscopy, so you could potentially handwave the collection of nanotubes at this point. However, that's not commercially or economically viable in the least.
The first method for producing CNTs ... in reasonable quantities – was by applying an electric current across two carbonaceous electrodes in an inert gas atmosphere. This method is called plasma arcing
Simplified, a good way to get nanotubes is to run electricity through carbon in a container full of one of several gases that had all been discovered prior to or during 1900. This method will produce them for you, but it probably isn't economically viable - you need run a lot of reactions to get even a small amount. It's not going to work on a city scale.
Other methods that produce more of a reasonable amount involve complex, powerful lasers, which I won't pretend would work here. Moving back electron microscopy is already enough of a change, so giant lasers don't really fit.
Your best bet may be "combustion synthesis":
In flame synthesis, combustion of a portion of the hydrocarbon gas provides the elevated temperature required, with the remaining fuel conveniently serving as the required hydrocarbon reagent. Hence the flame constitutes an efficient source of both energy and hydrocarbon raw material. Combustion synthesis has been shown to be scalable for high-volume commercial production.
This method seems plausible in the early 1900s, although its difficult to explain its invention so early. This is the closest you can get to what you want, and I wish you luck figuring out how to make enough.