"How can a sponsor file a BTD before data is in and fully analyzed?" The answer commensurate with the tone of "Indeed, an advanced reading comprehension test" might be: the same way a company could make financing contingent upon a designation it hasn't even filed for yet.
But a good, serious answer might be: Because the FDA doesn't require Phase 2 data in order to grant it. In fact it can be applied for "With IND or after" and "Ideally, no later than the end-of-Phase 2 meeting". https://www.fda.gov/downloads/Drugs/Guidances/UCM358301.pdf
"A. Qualifying Criteria for Breakthrough Therapy Designation" 3. Preliminary Clinical Evidence Unlike the information that could support fast track designation, which could include theoretical rationale, mechanistic rationale (based on nonclinical data), or evidence of nonclinical activity, breakthrough therapy designation requires preliminary clinical evidence of a treatment effect that may represent substantial improvement over available therapies for the treatment of a serious condition. For purposes of breakthrough therapy designation, preliminary clinical evidence means evidence that is sufficient to indicate that the drug may demonstrate substantial improvement in effectiveness or safety over available therapies, but in most cases is not sufficient to establish safety and effectiveness for purposes of approval. FDA expects that such evidence generally would be derived from phase 1 or 2 trials. Nonclinical information could support the clinical evidence of drug activity. In all cases, preliminary clinical evidence demonstrating that the drug may represent a substantial improvement over available therapy should involve a sufficient number of patients to be considered credible. However, FDA recognizes that the data cannot be expected to be definitive at the time of designation. Ideally, preliminary clinical evidence indicating a substantial improvement over available therapies would be derived from a study that compares the investigational drug to an available therapy (or placebo, if there is no available therapy) in clinical testing or from a study that compares the new treatment plus SOC to the SOC alone. FDA encourages sponsors to obtain some preliminary comparative data of this type early in development. Other types of clinical data that also could be persuasive include single-arm studies comparing the new treatment with well-documented historical experience. Generally, FDA expects that such historically controlled data would be persuasive only if there is a large difference between the new treatment and historical experience. For example, where lung function decline is a major manifestation of a disease, single-arm study data showing that a new drug significantly increases lung function could be persuasive if there is no available therapy that increases lung function. Data demonstrating that a cancer drug substantially increases overall response rate compared with historical controls (e.g., historical response rate with available therapy), with consideration of duration of the response, also could be persuasive. Sponsors contemplating the use of historical controls should consult FDA’s ICH guidance for industry E10 Choice of Control Group and Related Issues in Clinical Trials for more-detailed discussions.12