[Alex Lao] was recently in such a situation. His sister was getting married and he designed, built, and delivered twenty RGB LED table centerpieces in a rush. There were no prototypes made, and when the parts arrived all twenty were built all at once over a single weekend. These table centerpieces are illuminated by RGB LEDs and battery-powered, but have an option to be powered by a wall adapter.
[Alex] helpfully shared some tips on reducing the production risks and helping ensure results in such a limited time frame. His advice boils down to this: reduce the unknowns. For Alex this meant re-using code and components from a previous project — even if they were not optimal — so that known-good schematic and footprint libraries could be used for the design.
From one perspective, the PIC32 microcontroller inside each lamp is overkill for an LED centerpiece. From another perspective, it was in fact the perfect part to use because it was the fastest way for [Alex] to get the devices working with no surprises.
For an added perspective on needing to get production right the first time on a much larger scale, be sure to check out getting an installation made up of 25,000 PCBs right the first time.