I am sure you are aware that generally for issues related to IDOC we need to ensure that the partner profile is correctly configured in WE21.
The resolution of your issue could in the Partner Profile, outbound message type. On the details screen, for the maintenance of the message type there is a check box for triggering the IDOC immediately.
I hope this helps!
Check in NAST table if you have record for your invoice (object key) if you have none check in t° NACE / V3 / if all parameters are set. You can also try in VF02/invoice number/goto/ header/message to add manualy your output if missing ; an error message may help you there.
And for sure, if parameterized, INVOIC output needs to be linked to custormer. (VV31 or NACE/V3/output)