In a BPMN diagram, you'd use a "start event" symbol (a white circle with a fine border). A marker in the center of this circle can specify further what kind of event starts the process.
In your case, there are several candidates, and I suppose you're asking because you're hesitating between them:
- timer event (i.e. every day at 23:00, but here the timing does not seem to be fixed in your BPMS),
- message event (for a message received from a participant of the process, but your other system just tells to start and does not seem tp participate itself to the workflow),
- a signal event (i.e. some other process sends a signal).
Looking at your narrative it should be a signal start event, with a triangle marker:

If deemed useful, this website provides a quick overview table on all kind of events, with additional explanation on each type.