Working backwards . . .
. . . also called "reversed engineering" this method can work. The key is to start with the outer planets and progressively narrow down the periods when that planet can be in that sign. Pluto first will define a 20 year period, Neptune a 14 year period, Uranus a 7 year period, Saturn a 2.5 year period, Jupiter a 1 year period.
As you move down the scale of time in a sign, don't make the mistake of jumping to a conclusion --- you can be off by 12 years with a wrong guess of Jupiter, for example. Knowing the Sun-sign makes it easier to scan through an ephemeris as you can check just that one month for the other planet's positions.
The Moon will be the last factor to check and this will narrow it down to a couple of days. That is as close as you can get with this method.
There are prior posts in the Astrology Forum about "rectifying" a chart. Many approaches have been covered, the most complete one has not been addressed probably because it might be beyond the scope of interest and skills of many list members who are just entering into astrological studies. It seems to me that the man who developed that method was 'Gillman' if my memory is correct. His approach first determines whether one was born at night or during the day, then goes on to narrow down the time, sometimes within 10 or 15 minutes of accuracy. His method is an obscure one and not known to many, but has some merit at the minimum. Dave