As you said, if no one is aware of any facts related to his birth, then it is not understandable to make a horoscope, because one or two information is missing then it will do to make a horoscope, such as birth time or place is not known, then the astrologer tries something. But when no one knows the birthdate, in such a situation a horoscope cannot be made. It would be better not to be too worried about the horoscope. You can go to any astrology for more information.
If someone wants to make his horoscope for his future predictions or information, then instead of getting more upset, he can go to other people like some people with the help of people having palmistry or face reading, etc, and can get answers to future questions.
The final advice is that nothing happens in life beyond karma, so if a person wants to make a horoscope just because of his eagerness to know his future, then let me tell you that only the information of the horoscope is not always correct. Karma will determine your future and not the date or time of your birth.