Is it even possible that this is my baby? [Pregnancy timeline confusion]

Not sure if this is appropriate to post on this sub so, sorry if it isn't.

I (25M) had sex with a (20F) on July 14 of this year. I used a condom, and checked the condom for any breaks or tears after we were done and found nothing out of the ordinary. She was not on any form of birth control.

22 days later or 3 weeks and a day later after having sex (August 5th), she did blood work and an ultrasound. On her paperwork it says: "The patient's blood test results confirm pregnancy at 3 weeks gestation". Does "pregnancy at 3 weeks gestation" mean from the very same day intercourse occurred? Or does "pregnancy at 3 weeks gestation" mean from the time of implantation?

Implantation is essential to achieve pregnancy and most websites say it takes 6-10 days after fertilization to occur.

Essentially, what I'm asking is if it's even possible that I'm the father if we had sex 3 weeks and a day before she was "3 weeks pregnant"?

Edit: Her last period, if she's telling me the truth, was June 18.