When does the gate at the St. Maarten port close?

[Kirbyk48]

I am booked on a MSC cruise that departs at 2300hrs on Sunday Jan 23.  My flight arrives at approximately 1430.  I figure that it will be somewhere between 1600-1700 until I clear immigration and get a taxi to the port.  Does anyone know if the gate closes at a certain time?  I am concerned that I won’t be able to board because the gate is locked.  Thanks for your help.