How soon.. ultrasound question

Does anyone know how soon a trans vaginal ultrasound can detect “signs” of pregnancy? I had a 2 month follow up after a miscarriage in February last Friday 4/13, to see if any tissue was left over.. there wasn’t, but I got a faint positive on a pregnancy test yesterday. So this is a completely new pregnancy, but I’m noticing on the discharge papers from my doctor they deemed me “pregnant” days before I found out but didn’t mention this to me all during my appointment. Plus I’m even more confused because I only ovulated a week before the ultrasound... would they be able to detect something? Or do you think the “pregnant” status was a mistake?