Put on some +CHR clothes and there is a +5 CHA chem you can make. That should atleast make it possible.
You just answered your own question. It isn't just "success rate", it's "the set amount of success between X and Y". At least I think that's how it works. If it's yellow then that means "difficulty of at least 50%". If your max chance of success of 5 because of level 1 charisma then you can see the problem. There's 10 points in the stat so I imagine that's 10% per point. Green is most likely around the early double numbers, yellow in the mid area and read in the later, higher up numbers. A dice role at early numbers is still a dice roll at early numbers. And that's what low stats are going to be using until boosted up.
It's either that or the game sets an extremely unlikely dice roll to hit on the mid-higher numbers. In which case you'll be rolling a lot. Even then I'm not entirely such which method is used so you could be rolling for nothing. Fastest option is to dump stat points in charisma. You'll probably need 3. Maybe 2 if you use stat enhancement items.