You cannot do this with an attribute because they are just meta information generated at compile time. Just add code to the constructor to initialize the date if required, create a trigger and handle missing values in the database, or implement the getter in a way that it returns DateTime.Now if the backing field is not initialized.
public DateTime DateCreated
{
get
{
return this.dateCreated.HasValue
? this.dateCreated.Value
: DateTime.Now;
}
set { this.dateCreated = value; }
}
private DateTime? dateCreated = null;