The rising sign is the sign climbing over the eastern horizon at the moment you were born, which means it is the single placement most damaged by a missing birth time. It changes sign roughly every two hours, so a four-hour gap in your memory can move it two whole signs. You can still make progress, but you should walk in knowing which methods narrow the field and which merely rearrange a guess.
There are 360 degrees of the zodiac, and the Ascendant moves through all of them in a single day. That works out to about 1 degree every 4 minutes on average, though the exact rate swings with latitude and the sign in question. Signs of long ascension, like the ones that rise slowly near the equator-facing horizon, can take two and a half hours to clear. Signs of short ascension can pass in well under an hour. So the phrase 'about two hours per sign' is an average, not a rule you can lean on for an exact answer.
What that means practically: if your birth certificate says 4:30 AM and you are not sure whether that is rounded, the Ascendant is the first thing that becomes unstable. A 20-minute error moves it roughly 5 degrees, which is usually harmless unless the sign boundary sits nearby. A 90-minute error can move it more than a sign. Everything else on the chart tolerates that error far better.
None of these produce a certified Ascendant. They produce a shortlist, and a shortlist is genuinely useful because it tells you which two candidates to compare against your life.
The most defensible technique is to work outward from the Moon. The Moon's sign is knowable without a birth time as long as it did not change sign on the day you were born, and the Moon's position constrains what the Ascendant can plausibly be. Traditional astrologers also use the physical markers of the Ascendant: the ruler of the rising sign is said to show up in body type, the shape of the face, and the way someone enters a room. Treat that as a tiebreaker between two candidates you already suspect, not as a procedure that generates an answer from nothing.
Even a confident sign estimate does not restore your houses. Houses need the exact degree of the Ascendant and the exact degree of the Midheaven, and those in turn need both the time and the latitude. Two people with the same rising sign, born twelve hours apart on the same date at the same city, share a rising sign and share almost nothing else in terms of house structure.
It also cannot recover the Ascendant's aspects. If your Ascendant is at 8 degrees Leo versus 27 degrees Leo, it forms completely different relationships to the rest of the chart. An exact estimate is an estimate of the sign, not of the degree.
Start from what survives the missing time, then move toward what does not. Read the Sun, the Moon if the sign held all day, Mercury through Pluto by sign, and the aspects between the outer planets. These are real, and they carry a lot of the interpretive weight people expect from a chart.
Then add a provisional rising sign labeled as provisional. Never let a guessed Ascendant silently become a fact you build on. If you later find a birth time, replace the guess and expect parts of your reading to change.