Maybe that's when baby implanted?
Remember that scans are only an average and babies vary greatly.
My first daughter I got a very strong positive two days after period was due and a 2-3 weeks on a cbd. We did the deed 3 days and 1 day before ovulation as we were trying. I had a 28 days cycle with a 12 day luteal phase and still got a strong positive then.
She then measured behind til 12 weeks but was then 8lbs 2 at birth.
Dd2 we did the deed the day of ovulation (not trying, just a one off). Still a 12 day luteal phase. Much fainter bfp at 2 days after period due and only a 1-2 on cbd.
By 8 weeks she was measuring spot on but by 12 weeks she was measuring 3 days behind my dates.
She then continued to measure slightly behind and was only 6lbs 14 at birth.
Logically, dd2 should have been measuring behind at 8 weeks as she should have implanted later than dd1. I got a stronger positive with dd1 so logically she should have been measuring more ahead than dd2 at the same gestation.
What I'm trying to say is there is no point in getting hung up about every little reason why you think their dates are wrong. It's likely baby will either catch up or maybe just measure a bit small throughout. A few days won't make much difference to your due date and essentially the baby will come when it's ready anyway, whatever they or you make the due date to be.
Pregnancy tests can pick up a pregnancy up to 5 days before a missed period so it's not unusual at all to get a positive test when you got one 