How to get a horoscope chart made if no date of birth data available?

It is mentioned at many places in this context that there are some advanced methods which are used by the expert and knowledgeable astrologers to work back with some general information about the person, his name, parents name, parents age, place of birth if available, and approximate range of time or weather during which the person was born. We do not know how much it is really going to be effective but can be tried. Another thing which is a word of caution in this area is that there are some frauds also in the market who would make money by giving some horoscope in the name of the nearest correct but one should be careful with such cheats.

Without the date of birth and time of birth, we can't make any astrological chart. So don't believe anybody if they say they can give you your chart and that will be a money-making activity only.
They can't make your chart. But seeing your father's chart, your mother's chart and your brother's and sister's chart, some interpretations can be made. But how far it is reliable is not known.
But by seeing your hand, some predictions can be made by a palmist. There are many good palmists are available and you can try if you are interested. Some people will give you some predictions by face reading also.

Palmistry is a kind of science dealing with the prediction of a subject with the observation of the different lines appearing on the palm such as Life Line, Heart Line, Mental Line , Fate Line and other signs such as mountains, cross, triangles, squares etc. An astrologer proficient in the palmistry would reveal both your past and future with a fair degree of accuracy.
Then the Palmistry is connected with the old branch of astrology known as Nashta Jataka where the horoscope of the person is traced out through the prediction based on the palmistry. The astrologers further predicts the date of birth, position of the planets, position of navamansha, planetory cofugerations etc on the basis of Nashta Jataka.
Hence they employ twin techniques to get back the complete prediction of a subject firstly the palmistry and the same is aligned with Nashta Jataka to know his details of his date of birth, birth time and the year of birth. Though combining the two is a tedious process and the astrologer should be familiar with the both the branches of astronomical science to predict effectively of your future events.

There are a few options to make horoscope when the date of birth is not exactly known.
Situation1: Vague or unconfirmed information about birth date available:
Exact date of birth is not known, but some other background information or vague information is available. There can be confusion between one or two dates. For example people may remember the birth date by relating it to some major local events or they may know the month and star and sometimes the day of the week. In such cases, ether the date of birth can be confirmed by referring back to the Panchang of that month and verify and confirm the correct date of birth. Then the horoscope can be made.

Situation . When no data is available; date, month and year of birth are not known:
Then the provision is there to use the method of "Nashta Jataka' calculation or"Prasna Jataka' calculation. Nashta Jataka or lost jataka is made by resorting to Prasna method, which is based on the time of the querying person's arrival, his first words, his direction etc etc. Fort his knowledge and experience are necessary. The horoscope thus made is verified and fine corrected by verifying the main basic information gathered from the horoscope by checking that information about the native and his family. In case horoscope of close relatives like siblings or parents are available then that also is verified and correlated for cross checking the information seen from the newly made horoscope.
A learned and experienced astrologer can verify and correct a horoscope y 'purifying' it as per methods and guidelines prescribed in texts. Similarly such learned and experienced astrologers can make horoscope when the DOB is not known.
It is also believed that for a woman the date of attaining puberty is a significant occasion and from that a 'Rutu Jaatakam' is made . Rutu Jatakam is considered important as it is believed it can help predict the nature of events of a woman.

Horoscope is a product of astrological calculations based on the position of planets in the solar system, Moon, Sun, and the castellation positions in the sky at the time of birth of a person. Depending upon the time of birth, which is of course the basic parameter to start for horoscopic work for making a truthful and accurate horoscope. So in absence of the time and date of birth, it is not possible to make a precise one. What some astrologers do is they infer the approximate month or season of the year when a person was born and then take the horoscope of the parents and deduce many things from palmistry, forehead reading etc and then make an approximation about the future of the person and prepare an approximate horoscope and effectiveness of such a horoscope is anybody's guess.

How much important is the time and date of birth is that even for twins a difference of few minutes in their birth makes a big difference as we do not know what are the changes happened during that time in the zodiac circle overhead. So the planets position would slightly move this side or other side and constellations also appear to drifting in the sky due to Earth rotation around its axis and even a small change is enough to bring substantial changes in the horoscope making the life and fate of two twin bothers. These small changes are not perceptible to our eyes but are there and cannot be ignored if we believe in the art and science of the Astrology.

So there is no foolproof method, whatever claim be made by some experts in the field, for making a horoscope in absence of the crucial and vital data that is time and date of the birth.

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.

An exceptionally experienced astrologer might be able to find clues. Particularly if there is an ambiguous time length they can actually work with. There is a whole area of astrology called the Nashta Jataka or Lost Horoscope in which the person's horoscope is outlined with the help of several predictions related questions and rectification methods. It is relatively factual and works in most of the cases.

By this technique (Nashta Jataka) the horoscope is traced if the person does not know about his time, date and year of birth. An astrologer uses the prashna kundali along with other predictive techniques and analyses to compute the degree of planets, the nakshatra of Moon, date of birth, the position of navamsha, dwadashamsa, and other divisional illustrations etc. All accumulated data is to be corroborated by asking about different sorts of events that occurred in a person's life. However, It is a tiresome task for an astrologer.