I don’t think that this is possible without adding custom javascript. The problem is that a repeater sub field will always have the same value. You could probably create an acf/load_field filter and update the default value to the current time.
Basically I would look at this https://www.advancedcustomfields.com/resources/adding-custom-javascript-fields/ and I would add an append action that updated the field value through JS. I’d probably also add an action to the other fields to update the time when a change was made. There is also the problem that I don’t think that date fields can be made read only and you’d probably need to use a text field.
On the other hand, it may be possible using the date_time_picker_args filter hook listed on the javascript documentation.
