The most basic of vacuum tubes was discovered, rather than invented, by observation of the Edison effect, whereby carbon particles boiled off an early lamp filament showed a shadow of the other end of the filament where they adhered to the glass envelope.
This was first observed by Edison himself in 1875 and refined in 1883, and led to hypotheses of "thermions" that are emitted from a hot filament. These in turn led to assembling diodes, which used these "thermions" to conduct current across the vacuum between a filament and a plate, and from there insertion of a grid to create the first triode by Lee de Forest in 1906.
The glass blowing technique and materials to do this, however, existed from the earliest days of hermetically sealing glass vacuum lamps, which followed close on the first metallic filaments to replace the carbon threads of the first Edison lampts.
All this to say that, had the knowledge existed, triodes at least (equivalent to those used in early radio receivers and CW transmitters as well as for audio amplification) could have been made well before 1900, possibly as early as 1885 to 1890 time frame (I couldn't quickly find a good reference on when hermetically sealed vacuum lamps first appeared; they have have been from the first days of Edison's lamps).
A simple triode (filament, grid, and plate) can be made to provide good gain for audio (though you may need multiple stages, meaning multiple tubes, to get and audible signal or enough output power to operate a record cutting machine). Some were also suitable for longwave radio (lower frequency than modern AM broadcast band). There are several YouTube videos by Glasslinger that show the construction, not just of diodes and triodes, but even pentodes, replicas of commercial tubes from the 1900s to 1930s.
In respect to the voltage question, it was well known long before 1890 that battery cells could be added in series (the actual word "battery" derives from the way multiple primitive cells could resemble a "battery" of artillery, multiple cannons side by side). There is a Volta pile still in existence at a university (I've forgotten which one) built by Allesandro Volta himself that produces more than 200 volts, and the earliest radio sets typically ran on anywhere from 45 to 90 volts on the plates, supplied by dry cell batteries (of up to 60 cells), while the filaments were lit by one to six cell (2V to 12V) lead acid batteries that would be exchanged for charged ones for a small fee when exhausted.