Sam didn't want to be normal once she found out that she had powers, and she wasn't afraid of having them either - as soon as she found out she told Ruby that "something wonderful is happening", and followed the pod crystal out into the desert to find out more. She was convinced that she was going to be a hero the same as Supergirl, right up until the Evil Kryptonian Cult Lady did her whole "they-will-call-you-Worldkiller-you-will crush-your-enemies-without-mercy-and-burn-the-world-of-men-your-daughter-was-a-mistake-and-you'll-forget-her" thing, which was the point where Sam started to freak out about having powers.