Speculah:No Contract Needed
There is evidence that humans are able to use magic before being contracted. If this is the case, Kyubey's contracts may merely do one of the following:
- Provide leverage to amplify a human's innate magic, in the same way that humans use tools to leverage their physical abilities.
- Remove a human's natural self-limitations that restrict magic use. These limitations would correspond to the way the body prevents itself from using its full strength in order to avoid harming itself.
This theory explains how the incubators were able to discover magic. Kyubey's race would have noticed minor distortions in reality caused by emotional beings using weak forms of magic on their own, and investigated to figure out how that was happening.
In episode 12, Madoka was shown emanating a pink light around herself even before she had finished making her contract.
In episode 4, the factory window cracked for no apparent reason before Madoka threw the bucket at it. This suggests that Madoka can exert psychokinetic force when in an emotional state despite being an ordinary human.
While revealing the nature of soul gems in episode 6, Kyubey indicates that fighting witches while remaining in a normal human body would be merely impractical, not impossible. He states that soul gems are created to allow more efficient use of a magical girl's power.
Madoka's dream in the first episode was an accurate depiction of events in a previous timeline. Either Madoka possesses ESP, her wish in the other timeline granted this vision, or Homura (the only magic user who had knowledge of those events at the time) used magic to induce the dream.
See Human Soul and Magic for related speculation.