An individual bean sprout weighs about .75g, so to have a weight of 300g of bean sprouts, you'd need 400 individual bean sprouts. A bean sprout occupies around .5cm cubed. Its cubic capacity therefore is half a cm. The cubic capacity of a standard American cup is 236.6 cm cubed.
A cup this size has the space for 473.20 individual bean sprouts at around .5 cm cubed capacity each. So, that would give you a weight of 354.90g. We work this out like this:
Capacity of cup 236.6cm cubed divided by capacity of individual bean sprout at .5cm cubed = 473.20 bean sprouts fit in the cup giving a collective weight of 473.20 x .75g = 354.90 grams of bean sprouts.
You could say that one standard American cup size will yield approximately 354.90 grams of bean sprouts. However, you must allow for the fact that, unlike liquids, bean sprouts can not be packed closely together. There are spaces, or air pockets between them. Therefore, as an estimate, lose the 54.90 grams and round 1 cup of bean sprouts down to the equivalent of 300 grams.