Generally speaking, about 99% of pregnant women can get a positive home pregnancy test within 3 days of the fertilized egg implanting in the uterine lining. The trouble is, it's so hard to tell when that happens!
Ovulation is an individual pattern for every woman, but to be very general here, it's about 2 weeks after you start your period if you have a "regular" 28-day cycle. 6-12 days after that, implantation can occur - so it could be 3 weeks after your period, or it could be more like 4 weeks. Every woman is different! This is why people will tell you to wait until you've missed your period, if you implant on the late side, it could be 4 weeks (when that next period is due) before there's enough hcg for a test to pick up.
Then, for even more complication, about 1% of women don't produce hcg as quickly. It's not dangerous to you or the baby - but it can be very frustrating, because you can be pregnant and late for your period and STILL not have enough hcg for it to show on a test. Some women have had to wait as long as 4 weeks AFTER their missed period to finally get a positive test! It's not common, but it does happen.
So, unfortunately, there's no straight answer to your question. :) Good luck!