I've learned that starting a sentence with a subordinating conjunction such as "if" there must be a dependent and independent clause. So to me the sentence,
If not, we do not need to start its procedure.
is ungrammatical. I'm getting tripped up by the fact "If not," could be a parenthetical phrase.
I was hoping someone would help me differentiate.
Note: The referenced example is found in an ETS dataset "of sentences with ordinal labels for grammaticality." https://github.com/EducationalTestingService/gug-data/blob/master/gug_annotations.tsv