The adoption of generative artificial intelligence in the public sector has been treated predominantly as a technological problem, with the expectation that productivity gains would follow from increasingly capable models. This paper argues, drawing on two auditable cases in the Brazilian Public Service, that the determining barrier to adoption observed in these units was not technological but training-related, and describes the four-layer structured pedagogical methodology developed by the author. The method was applied in two units with distinct institutional profiles: the Sectoral Internal Control Office of the Federal District Department of Health (SES/CONT) throughout 2024, and the Internal Control Unit of the Federal District Department of Economic Development, Labor and Income (UCI/SEDET) throughout 2025. In both cases, the official indicators from the Electronic Information System of the Federal District Government (SEI-GDF), verifiable by third parties, recorded substantial gains: average processing time fell by 18.2% at SES/CONT and by 50% at UCI/SEDET, with UCI also recording a 92% increase in technical-report production, the issuance of 288 formal recommendations to public managers, and the review of cases whose financial volume totaled US$ 104.3 million (the value of the cases reviewed, not an estimate of funds saved). In neither unit did internal control mechanisms identify any information-security incident, sensitive-data leakage, or formal compliance challenge from external oversight bodies during the period examined. The analysis is consistent with the hypothesis that the method is portable across agencies with distinct mandates, operates within protocols designed to comply with international and national data-protection law and with the principles of public administration, and is accessible to public entities under budget constraints, since it used free AI models.

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