A)- Direct in a seed raising (soil) mix.
B)- Drowned in water too long, there is no need to soak them in water.
I have found through extensive experiments, pre sprouting seeds in paper towel and then transplanting them actually delays growth by 2-5 days on average, compared to sowing them directly in soil.
Using tiny cups with limited soil is also not conducive to good root development, the cups are just waaaay too small.
Just because "everyone else does it" does not make it right!
Pots about 4 inches across and 5 inches deep are much superior and provide enough room for 3 weeks of development, easily.
If you want to see the root system of a 3 week old seedling and why deep pots are so important, go to week 7 of my diary "cannabis conundrums" and you will find many pictures of this. This might give you an insight as to why tiny cups are totally inadequate for anything more than 3-5 days of growth.
Buying decent plastic pots may cost more, but with a bit of care and washing between cycles, will last many years and reduce garbage going to landfill dumps, making them far more environmentally friendly too!
Hope this helps, Organoman.