You can set up a (https://support.docusign.com/guides/ndse-user-guide-data-validation-for-text-fields) validation for the text field, such that it's only valid if the date is today or later. Look up a regex library for the specific expression you should use.

Hope this helps.

 Yes, this is possible.  To make this work you will need 2 fomula fields, 2 text box fields and a date signed field.  Make sure to format your fields with clear naming convention.

1. Name first Formula DateofCareFormula.  Change the font to white.

2. Name second Formula DOCTest.  Change the font to white.

3. Name first text box "DateofCare" and add date validation to the field.

4. Name the second text box "DOCMessage".  I added the following message to mine, "Date of care cannot be prior to the date signed."

5. Name your Date Signed field as "DateSigned".

6.  In your DateofCareFormula use the following formula:  DateDiff(aDateSigned],SDateofCare]) Change the decimal places from 2 to 0.

7.  In your DOCTest formula use the following: lDateofCareFormula]>0  Change the decimal places from 2 to 0.

8.  Select your DOCTest formula and create a rule under the conditional Logic tab.   Make the trigger field =1 and click the text box named "DOCMessage", then click Done.

9.  Save your changes, then test your template.  The message should show every time the date of care is prior to the date signed.  I know this method works because I have used it prior.  Moreover, DocuSign offers webinars that teaches you how to use advanced fields, conditional logic and formulas.  I have taken these in the past.  For the most part, it is a review for me.  However, you do learn useful things like the example I provided in the webinar. 

I hope this helps