You can, but only for a handful of characters.
Currently, you can only get these characters for free by playing the game:
- Amber (unlocked through story)
- Kaeya (unlocked through story)
- Lisa (unlocked through story)
- Barbara (reach Adventure Rank 18)
- Xiangling (clear Spiral Abyss floor 3–3)
Sometimes, the game also give you free characters through events, where they gave a bunch of characters previously, like Fischl, Diona, or one of Liyue’s *4 characters.