Without a birthtime there’s no way to cast a chart with an accurate ascendant. Because of that there’s also no way to know where the house cusps are. The other consideration is the placement of the Moon. Since the Moon moves about 13 degrees in a day it can happen that you’re faced with two possibilities for the Moon sign. Because of this I first cast the chart with a birthtime of midnight on the morning of birth. That way I know where the possibilities start.
If the midnight chart shows the Moon in early to mid degrees there’s no need to look further, you have the Moon sign. If, however, it’s mid to late degrees I cast a chart for 11:59 of the day and see if it changes signs. In any case you can see the span of where it might be. At that point you can switch to a chart for “unknown birthtime,” so as not to be distracted by elements that are not known, such as an arbitrary rising sign, angles, house system, vertex or part of fortune. I tend to look at the midnight on the morning of chart and just ignore the arbitrary bits as it’s actually less visually distracting to me.
When I analyze the aspects the moon may make I take into account that loose 13 degree movement and adjust accordingly. If the Moon changes signs during the day it can be helpful, if you know the person involved, to try to rule out one or the other Moon sign. For instance, there’s a distinct difference between a Sagittarius Moon (Jupiter-ruled) and a Capricorn Moon (Saturn-ruled). Are they generally cheerful or stoic? Do they love adventure or security? One thing to keep in mind is the possible aspects to the Moon that might affect this judgement. If the Moon set in Sagittarius aspects Saturn or the Moon set in Capricorn aspects Jupiter, that could throw the analysis off. I find it most helpful to take a best chance stance and keep an open mind.
In any case, it’s a fun astrological puzzle that can help you stretch your analytical muscles.
How do you approach charts without birthtimes?