Hi,
Without seeing the configuration of both the feature layer and the dashboard it's hard to ascertain exactly what's going on.
Would you mind posting a screenshot of the date field not being selectable as a target field? It would also be worth checking to see which fields are selectable as target fields as Category or Number selectors.
Additionally, it might be worth creating a new Hosted Feature Layer using one of the AGOL Feature Layer Templates (e.g. Debris Reports) which comes with a submitted date field by default. If this can be added as a component in the Dashboard (e.g. a Pie Chart) and then configured correctly in the Date Selector this would point towards the date field in your original Feature Layer perhaps not working as intended.
Hope this helps get to the bottom of the issue for you.