The ADXL362 will default to a particular configuration on power up. If this is not exactly the mode you want, you will need to configure the part using the MCU. Is your MCU powered down until the switch closes? You might be able to manually stimulate the ADXL362 and quickly program the part while the switch is closed. This is definitely a chicken and egg situation.
Do you have a block diagram you could share?
On power up, the activity/inactivity functionality is disabled, but the chip boots is default mode (Link/Loop bits being 00). This is not useful anyway, let me know otherwise. If you guys designed this chip to be used for a motion activated switch, then this is no use really. What is the point in paying such a huge price per chip and not being able to achieve the desired application? The only possibility which can solve this is to map the AWAKE bit (Status Register) to either INT1 or INT2 pin on boot up. The AWAKE bit comes alive with a value 1, which when mapped to either of the INT pin can solve this issue (The default values of reg 0x2a or 0x2b must be 0x40, not 0x00). I hope AD incorporates these changes in the existing chip immediately.
I can get this solved either by a mechanical switch or a tiny PIC MCU always powered - both of which is not at all elegant (increases cost+complexity).
Below is the block diagram.