According to PEP 557 which defines the meaning of data classes,
The dataclass decorator examines the class to find fields. A field is defined as any variable identified in __annotations__. That is, a variable that has a type annotation.
Which is to say that the premise of this question (e.g. "How can I use dataclass with a field that has no type annotation) must be rejected. The term 'field' in the context of dataclass necessitates that the attribute has a type annotation by definition.
Note that using a generic type annotation like typing.Any is not the same as having an unannotated attribute, since the attribute will appear in __annotations__.
Finally, the helper function make_dataclass will automatically use typing.Any for the type annotation in cases when only an attribute name is supplied, and this is also mentioned in the PEP with an example.