You have downloaded the W4 form from here.
You are trying to add a Date at the bottom of first page just above the label '10 Employer Identification Number (EIN)'
If you check this 'Employee's Signature & Date' both labels do show a colored box next to them. Which states that these 2 are not form fields.
Even if you would like to Sign and add date here using Acrobat Reader DC.
Then open the file in the Reader DC app. Click on 'Comment' tool from the set on the right.
This will list all the comments tool on the top of the document. From here select 'Text Comment' tool as highlight below.
After selecting this tool you can add the date.
Once that is done close the comment tool and click on Fill & Sign.
From here you can sign the document.
Let me know if this works for you.
Unfortunately, when you save the document, the comment is hidden. How do you add text that is readable as a sendable file?