There are several possible things you can do then - some you won't like!
1. Draw your game at full screen from the off - 1920x1080 is an awful lot of drawing though.
2. You might be better off sticking to a "standard" sized screen and using that as a virtual screen then display that centred in the middle of the full screen. So you'd do something like this (non-tested code)
GLOBAL actual_x, actual_y
GLOBAL required_x, required_y
GETDESKTOPSIZE actual_x, actual_y
CREATESCREEN 1,999,required_x, required_y
USESCREEN 1 - Virtual screen
// Draw all your stuff
USESCREEN -1 - Actual screen
DRAWSPRITE 999,(actual_x-required_x)/2,(actual_y-required_y)/2 //(or use POLYVECTORS)
That should (not tested, maths could be shonky) draw everything to the virtual screen (number 1 - sprite number 999) and then display it on the actual screen, centred.
If you use the POLYVECTOR method (which would be advisable), then you can scale down the actual screen to fit ANY device and it should be pretty smooth too, as well as fast. It will also do the opposite too, and allow you to scale up your screen (although scaling up alwayss looks worse than scaling down).
[EDIT] Made the main loop clearer.