The typical room temperature current is as follows, measured at 5V DC input:
CASE 1 –  Full bright “xbb 255”, blank screen: 238mA
CASE 2 – Full bright “xbb 255”, checkerboard screen: 243mA (the checkerboard pattern alternating white and black pixels is worst-case panel power)
These are typical numbers. We quote the absolute worst case (400mA) on the datasheet; it is improbable that all parts of any particular module will be the worst case.
See the inrush power on applying power to the module in the image below.
This surge charges the tantalum capacitors on the board. The module contains a supervisor reset chip MCP809T with a minimum delay of 150mS from power. So as long as the caps are charged in 100mS, all will be well. You could easily limit the inrush current to 400mA and be okay.