What is the volume, in ml, of the Covid-19 vaccine?

One dose= 0.3 mL

0.3*330*10^6= 9.9*10^7

9.9*10^7/10^6= 99 m^3

US population is about 3.3 x 10^8 persons and that quoted dose of 3.0 x 10^-1 ml is 3 x 10^-7 cubic meters. [...since (1 cm)^3 = (10^-2 m)^3 = 10^-6 m^3)]

Multiply: (3.3 x 10^8 doses) * (3.0  x 10^-7 m^3/dose) = 10 x 10^1 m^3

About 100 cubic meters.

That's the volume of the diluted vaccine that's actually injected.  Look at the FDA guidelines at:

https://www.fda.gov/media/144413/download

...and you'll see that each vial contains 0.45 ml of frozen suspension that will produce 6 doses, making each dose 0.075 mL of undiluted suspension.  So the volume of vaccine as shipped is about 0.3 / 0.075 = 1/4 of the injected volume.

So, if you're looking for the volume of vaccine that is produced and shipped, that's "only" 100/4 = 25 m^3.