I hope someone else has a better idea, but you could create an excel spreadsheet with a cell containing the function =TODAY(), then place that cell after setting the prefs to link to text and spreadsheet files. I suspect you'd have to open and save the sheet each day to update the date, but then the ID file should ask to update the link.
Currently on CC2014 but I've used this variable for several years. Check the Define section. I seem to recall that I had to create the variable for Current Date.
It doesn't allow it. In the define section you can define a new variable but it has to be based on one of the coded ones. So you can create a new Modification Date variable, Creation Date variable, or Output Date variable. It changes the format but not what it does. It doesn't allow you to create a new type of variable just a new format of an existing one.
Create a new variable based on Output Date or just use Output Date as your variable. When you insert it in your InDesign file it will have a place-holder date but when you print the file (or create a PDF) the date will change to the current date.
OK, here is the step-by-step instructions that should work all the way back to CS6 (longer if I remember correctly).
First, you could use one of the pre-defined variables, but I want you to experience this from bottom to top.
Go to Type > Text Variables > Define. This opens the Text Variables dialog box.
Click New. This opens the New Text Variable dialog box.
Name the Variable something like "The current date for printing."
Choose Output Date
You now need to format how the date is inserted. For this exercise we're going to choose Time > Hour, then insert a colon, then Time > Seconds, then Month (Name), then day (number), then year (number). Inserting the time and minutes will help us see how the variable updates. (Much better than waiting for the next day.)
As you enter the codes, you'll see a preview of the result in the Preview field. Now, the Preview may not show the "current" time. Don't worry.
Now click OK to close everything up. The text variable you created with be in Text > Text Variables > Insert Variable >
When you insert the text variable, it will appear in the text with its preview.
But here's where it's going to confused you. This preview shows the last time the document was printed or output as PDF or when the document was first created if it was never output. That's the LAST time. InDesign can't tell the future, so it doesn't know what time or date it will be when you eventually output the file.
So, try an experiment. In my case, I'm going to create a PDF. Even though the text variable SAYS 5:21, the clock on my machine says 5:36. So let's see what the PDF shows.
That's how you can get the "Current Date" to be inserted when you print the file. The preview changes at the time of printing.