After the circuit board was designed, printed on photo paper, transferred onto copper and etched, it was a quick process to solder 7 LEDs onto it. Soldering took about 15 minutes start to finish and I imagine this could be done much faster if you can use a reflow oven instead of hand soldering each component.
I was impatient and soldered only 4 capacitors instead of 7 because I knew that this first prototype won't be chained together with other displays.
Here is how the populated circuit board looks like:
The lesson learned here was to create bigger pads for the Neopixels which will be taken care of in the next iteration of the PCB design.
I don't know if I need bypass capacitor on each and every LED or if putting one 10uf cap per 7 Segments would suffice so if you know the answer to that question, please let me know!