Can I use Raichu V's "Fast Charge" attack during the game other than on my first turn?
Yes, you can. The text about "if you go first" is in addition to any other turns during the game.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH9_45
SWSH9_45