I'm not a professional, but I used to do this in order to understand the correct time of a few charts.
If you have the day right and more or less the part of the day ( morning, noon, evening, night) you can use an app to track the ASCENDANT line and ask yourself questions based on the relevance of the Chart Ruler that results with each sign, after that you'll want to look at each individual astrological house and understand if the planetary positions captured within make any sense based on your life-experience so far.
Sometime extreme differences between a planet being in a house rather than the other (like between 1st and 12th) can really help you a lot in pin-pointing your birth time, expecially if let's say those planets are in proximity or same sign.
Also take into consideration your intuition during this process, I'm pretty sure the Gods and Daemons would help out since it's quite important.
Anyhow the above is something I do where I really have no other way in determining the hour of a Birth Chart.