A standard urine-based pregnancy test turns positive ~10-12 days after conception. So the embryo must’ve been even younger. Probably 3-6 days.
Conception happens in the Fallopian tube, it takes 2-3 days for the fertilized egg to reach the uterus for nidation.
From a hormonal level, a pregnancy is undetectable, because literally nothing happens in the woman’s body at first. The increase in progesterone happens after every ovulation. The embryo isn’t connected to the mothers blood stream yet. And you can’t see on an ultra sonic scan whether the egg is fertilized or not.