The hormone that is produced in early pregnancy is HCG, or human chorionic gonadotrophin if you want the long and complicated name. HCG is released by a developing embryo and by the placenta later on in pregnancy, as it takes over the function of sustaining your growing fetus. At-home pregnancy tests use HCG levels as an indication that you have conceived, and therefore, the levels of this hormone produced in your body need to be high enough to register on a test before you will be able to get a positive. Some women produce higher levels of HCG immediately after an egg was fertilized and started implanting itself into the lining of the uterus, but as a rule, the majority of newly pregnant women can get a positive pregnancy test on the day their period was due.
Highly sensitive pregnancy tests are more and more accurate, which is probably why they are growing in popularity. If you suspect that you are pregnant and really don't want to wait, you can try with one of these. But be aware that even a negative pregnancy test does not mean you did not conceive if you take it at any time before your menstruation was expected, even with highly sensitive tests. To be on the safe side, testing on the day of your missed period or a few days after produced the most reliable results. The added bonus of taking a pregnancy test when you have already noticed another pregnancy symptom your missed period itself means that you have a real indication that you are expecting a baby!