If the date/time prompt (or date prompt) is not set, it would default to current date and 12:00 (Current date as is on your personal client machine, if you select it to change time it'll be current to complete clock settings.)
Here is some code to get to a date prompt (not date/time), it might prove helpful (the prompt name is called 'PromptDate'):
<script>
var dDate = new Date();
//Subtract one month
dDate.setMonth(dDate.getMonth()-1);
//Set to first of Month
dDate.setDate(1);
//setValue adjust current date in prompt
pickerControlPromptDate.setValue(getFormatDate(dDate, 0 , 'YMD'));
</script>
Include this in an html item after the date prompt. This script will assign the first of the previous month as the date ( Date: March 19th prompt would show Feb 1)