No official date has been announced yet. The most recent information indicates the beginning of 2024. The most recent press release is in Japanese, Cy West was appointed as a general manager of Nagasaki Marriott. Cy West is from London, England and his career profile is:

March 2000: Started a career in the hotel hospitality business in the U.K.
June 2007: Overseas operation at Hilton Worldwide
December 2012: Global sales at Marriott International. Regional Director and Area Director. Sales and distribution strategy at Marriott hotels in Japan and Guam.
April 2023: Nagasaki Marriott General Manager at JR Kyushu Hotel Management. (JR Kyushu Hotel Management operates Nagasaki Marriott)

The recruitment for Nagasaki Marriott has started. Plan to have 130 employees, 100 full-time employees, and 30 part-time employees. Recruitment details are:

Operation: about 30 positions
Cook: (western cook, about 15 positions; sushi and teppanyaki, few positions, bakery and pastry, few positions)
Sales and marketing: few positions
General Affairs (HR, accounting, purchasing, IT, and engineering): few positions

The employment start date is October 2023. I am guessing that all other positions will be filled by transfer from other Marriott hotels.

News Release by JR Kyushu Hotel Management (PDF in Japanese)