How could I create an expectation to say the time value in a field should be later than some number of hours ago?

You can use this expectation: expect_column_values_to_be_between

The max_value argument can be left unspecified (left as None).
The min_value is the argument that should express your constraint. However, you cannot set it to a specific numeric value, since what you want it to say “at least X hours ago”. This can be achieved using Evaluation Parameters. They allow to set an argument of an expectation to a variable (evaluation parameter) and provide the value at the validation time.