I used Abdurrahim's suggestion. However, it seemed to give a weird time format and also added the abbreviation for the day as part of the build date; example: Sun 12/24/2017 13:21:05.43. I only needed just the date so I had to eliminate the rest using substring.
After adding the echo %date% %time% > "$(ProjectDir)\Resources\BuildDate.txt"
to the pre-build event, I just did the following:
string strBuildDate = YourNamespace.Properties.Resources.BuildDate;
string strTrimBuildDate = strBuildDate.Substring(4).Remove(10);
The good news here is that it worked.