An accurate birth time gives you a more complete picture, but you can still cast a valid chart without it. You may calculate the chart for either noon or sunrise on your day of birth. If you were born in the United States, your time of birth is probably on record in the state where you were born.
Most states have an office responsible for vital statistics.
Some will give you your time of birth on the phone, but others require you to order your birth certificate. If you order your birth certificate, make it clear that you want the time of birth displayed. Otherwise, it may be omitted. If you were born outside the United States, contact the government office in your country that keeps birth records. It takes a lot of work to calculate an astrological chart by hand.