Hello!
There is currently no support for a date picker with time. However, this could be a great plugin! I have added a
feature request in blockly samples for this. Feel free to add any additional information if you think it would be helpful.
The closure datepicker- which is what we use in the date field- does not have an option to set the time. You would need to add a way for the user to set the time in the dropdown yourself. You could do this by either adding html elements and css to the current date picker, or by finding a date picker that includes a time picker. Alternatively, you could create a separate time picker field and add this as well as a date picker field to your block. Either way, I don't think you will be able to get around creating your own custom field.
Hope this helps and feel free to respond if you have more questions!
Abby