Can a woman be born without a womb?

Yes. General abnormal development can cause this. One specific condition comes to mind and that is androgen insensitivity syndrome (AIS). In AIS individuals produce, but don't respond to androgens, male hormones like testosterone. The result is a person who is genetically XY will develop into a girl, and then grow into a full woman. For all intents and purposes she is a woman. A simple genetic test can determine if AIS is present.