In the late 1920s ...
A single Electric carbon microphone model 387 would be amplified to drive a portable disc-cutter, perhaps run from AC power, but also when AC was unreliable, run by DC batteries to cut the wax blank masters.
(WE had the monopoly on electrical recording technology well into the 1930s - bigger companies like UK Columbia, Victor, and German Grammophon developed independent systems, thus
avoiding the per-disc royalty WE collected from anyone who licensed their system)
The band would be arrayed so that softer instruments would be closer to the microphone, louder ones further away; a drum trap might be used, with a tuba substituting for a string bass. Experienced engineers/experts would know how
to set up a room on these lines, including how to include a vocal soloist in the 'mix'