United States-Taiwan Initiative on 21st-Century Trade First Agreement Implementation Act This bill expresses the approval of Congress for the June 1, 2023, agreement regarding trade between the United States and Taiwan. The bill also imposes requirements on the negotiations of certain further trade agreements between the United States and Taiwan. (The June 1, 2023, agreement, which addresses issues such as customs administration and regulatory practices, is the first of several expected agreements under the United States-Taiwan Initiative on 21st-Century Trade.) The June 1, 2023, agreement may enter into force no earlier than 30 days after the President certifies in writing to Congress that Taiwan has taken measures necessary to comply with the agreement. The bill also imposes requirements on the negotiation of further agreements under the United States-Taiwan Initiative on 21st-Century Trade, such as requiring the U.S. Trade Representative (USTR) to (1) share any U.S. negotiating texts with Congress prior to sharing the text with Taiwan or any parties outside of the executive branch, (2) share any negotiating texts from Taiwan within three days of receipt, and (3) provide daily briefings to certain Members of Congress during negotiating rounds. A further agreement shall not take effect unless (1) the President, at least 60 days before entering into the further agreement, makes the text publicly available on a USTR website; and (2) a bill is enacted into law expressly approving the further agreement.