Can anxiety depression suddenly develop without a trigger?

Yes. Lots of medical issues can cause this. See your family doctor to rule out things like thyroid problems. If medically cleared, have a psychiatric evaluation. Many psychiatric illnesses are biological illness that seem to come out of nowhere. This is not your fault! and there is help!
At times, yes. Anxiety and depression have genetic predispositions in some families or individuals. Most anxiety and depression have a stressor or trigger that brings it to light.Folks with no genetic load tend to resolve the two fairly quickly without help. On occasion there are no known triggers. A genetic load drives them. Triggers plus genetics seems to cause the most severe responses. Family history rules.