In the olden days, most of them were not having birth date and time. so, it is not a new problem rather it is accepted as a common situation. It is very much acknowledged in the Vedas and a separate section is dedicated for it.
It is called Prasna Lagna. the time of asking a question to an astrologer for the horoscope. one can make the chart and do the predictions. while calculating the Dasa times one has to go backwords till the birth year of the person and then tell the different events that might have taken place. In this way, we can verify!
I have done many horoscopes in this manner and the results were astounding. Therefore, don't get discouraged if your known people are not having the birth time or date, here is the way. astrology addresses such issues as well.
Thank you for taking the time to read this lesson!