Next time before starting the APU you can have a look at what it's doing by selecting ground test enable swith then select the CMC on CDU select EICAS Maintenance pages, go to 49 APU select display and on the lower EICAS you will see
Note the door is shown closed in the first pic.
Then when you select the APU master switch to on will see after a few seconds Door will be open
(this pic shows the APU at 100%, it is for illustration of the door position)