It takes Toyota 16 to 18 hours or so from start to finish on a car, with around 35 total man hours of labor put into each.

I think a custom vehicle ordered from a sales outlet, could be completed within 2 to 3 days, and shipped out, available to the customer within 7 to 10 days.

It would require pushing manufacturing forward in numerous ways, and retooling the entire process of making a car for this business model, but there's no reason that can't be done. It would already exist if the laws allowed for direct sales.

Except that the factories are already booked out several months in advance. Manufacture of a car takes less than a day, delivery can be done within a week, but that doesn't help if the nearest available slot in the factory is 4 months away.

A problem that would be immediately solved if it meant losing direct to consumer sales...

In Germany when you order a car at a car dealer you usually have to wait several weeks or months until you get your car. Obviously depending on the backlog in the factory.