If you know the day of birth and the place
(exactly) but not the hour, it's no real
problem to find the time within a pretty
narrow range. Every two hours a new sign
rises, goes through each degree of the sign,
and then a new sign rises. A good astrologer
should be able to figure out your rising
sign, within a few degrees (and at least
within ten degrees, which is 120/3=40 minutes
of clock time).

Your displacement from these facts would also
help the astrologer to place your chart
correctly.

The rising sign and the moon are two very fast
indicators in a chart (they change a lot over
very short times) and between them and house
placements (by examining life issues) it's not
all that difficult to converge on a time of
birth. A lot better than guessing out of the
entire 24 hours of the day.

This all is true for people who believe they
'know' when they were born; if the chart is way
off (rotated) it won't make a lot of sense to a
good astrologer, who will then rectify it. Often
the mistake (now uncovered) will be verified
by the triggered memory when the person tells
family and friends what the corrected birth time
should have been (if it wasn't recorded properly).

Some say you can regress and look at the clock
at the moment of birth -- I'm not sure how that
is supposed to work but that's their area of
expertise.