4 dpo?!

Can you get a positive pregnancy test at 4 dpo?! I didn't think it was possible. Here's my story: 
My LMP was March 23-28. Normal flow, cramps etc. Found out I was pregnant April 10, meaning ovulation would have occurred the 6th. I have missed my April cycle now. Nausea, heartburn, everything is in full blown mood. My LMP before that was Feb 13. Everything I have googled about implantation and conception doesn't match up. Example (I'm 4 weeks and 3 days, meaning I found out at 2 weeks and 4 days)