Me and a friend of mine play this a lot and we had to explain it a bit to a new player, so we also had to give the USSR an advantage because it would be first time player against a veteran.
We found that there are three ways to make this a bit more fair:
- Give the USSR more starting influence to divide (this can be in Eastern Europe or in any other continent)
- Give the USSR some starting points, that way America has to accumulate more points to win the game, I think that 5 or 3 is fair but you can choose that for yourself
- In the first headline phase: USSR plays a card and America doesn't, this can give the USSR an advantage if they have good cards so it's a gamble.
EDIT
- You could also give the USSR player a partial mulligan, discard the cards he doesn't want and let him pull that many new cards