/**
 * @param args the command line arguments
 * @throws java.io.IOException
 */
public static void main(String[] args) throws IOException {
    File file = new File("");
    PDDocument doc = PDDocument.load(file);

    doc.removePage(0);

    doc.save("");
}

Opens a PDF Document, removes the first page and then saves the document

PDFBox: Remove first page of a document

Java