It can be figured out (rectified). I've successfully done it for everyone in my family since they don't believe in astrology so I couldn't really ask for their birth times... plus most people don't know when they were born. And I wanted to know their charts.
It can take a while of going back and forth with your chart... fiddling around with it. To rectify, use https://alabe.com/freechart/ and not astro.com. Alabe lets you just click on the back button to change the time and then submit for a quick new chart. Astro.com takes too much time to change birth data, and when you have to go back and forth dozens of times, you'll want to save some time.
So to rectify... make the chart with your approx time of birth. Or just noon if not known at all. Look to see where the planets are, compare the info on planetary placements on Azazels astrology (or just your own knowledge, depends on your astro level).
Look at Pluto, which rules our obsessions. Does the house it is in match up with your personality and life? If yes, now look at Mars, where our energies go. Does this match up? Look at Saturn, where our hardships are. Does it match up? If any (or all) do not, then click the back button on your browser, enter a new time based on what house you think any of these planets should be (change it by an hour for a slight variance or even by 20+ hours for drastic variance), and click on "submit". Look at the new chart. Does this match up? And then look at the other planets. You'll need to spend time tweaking it until it's
just right, you'll probably find yourself fine-tuning it by changing it by just a minute or two at a time.
The reason I look at Pluto, Mars, and Saturn first is because these aspects of our lives (and the lives of others) is easiest to see. Glaringly obvious, in many cases. Moon, as well, since that's where our emotions are. But keep in mind the nature of the sign the planet is in, don't let that alone make you think the house placement is accurate or not. For example, Moon in Cancer is very similar to Moon in 4th house. So keep in mind that just because your Cancer Moon sounds like the description for Moon in 4th house, your Moon probably is not in 4th house (1 in 12 chance). Blend the two: planet in sign and in house.
So you're going to be going back and forth a lot until the chart makes sense. Once it does, then test it out. Look at when the outer planets transited the houses over your past few years. Do they make sense?
For example: With your new chart and test time, if Saturn is transiting the 2nd house and you are noticing these effects (finances suck), then this may be your correct time. Are you currently focusing on your career? Look to see if Pluto transiting the 10th house of the chart with this birth time. Did these transits take effect in your life around the time the planets entered the houses? Did you make a long distance move recently, or a decade ago? Look to see if Pluto crossed the IC (4th house cusp) around that exact time. A marriage, look to see if any outer planets crossed the DC or aspected the ruler of your 7th.
These are just examples and many other factors play in, but this helps give an idea. At the time Pluto was in my mother's 5th house and conjoined the ruler of her 5th house, I was conceived (her first child) and at the time it retrograded and conjoined again, I was born. This helped verify to myself, that I had figured out her correct birth time, as Pluto aspecting the ruler of the 5th is often seen when one has their first child.The first time she moved internationally, Pluto conjoined the ruler of her 4th house. If I had a different birth time set for her, these would not have made sense. I hadn't even known her approximate time of birth.
This is why if you look online, many astrologers charge a lot of money to rectify charts. It can take days of emailing back and forth and asking personal questions. It can be very time consuming, unless you luck out right away. Be prepared to spend quite a while rectifying your charts. I spent time over the course of a few days figuring out one chart, and it was someone I knew quite well but she had a long and eventful life. This is not always the case though.