You can use Model Action in the Model for that. The trigger will be, whenever a new row is created then set the action as Update a field on the row(s) the ‘Date field’ as Today.  Hope that helps.

You can also remove the ability to inline add records and use a global action on the table. Have this action create a new row and set default fields from there. 

Craig’s idea is the most straightforward — just add a Global Action of type “Create new row”, and then you can specify default values for specific fields on the new row. You can specify default values for Date / Datetime values using special values such as “Today”, “Tomorrow”, “Yesterday”, etc., or pull the value from a field on another Model, or specify a specific Date.

Thanks!