Our first appointment is tomorrow! We're so excited but anxious too.

Based on my last period, they estimate I'll be 6w6d tomorrow. Based on the earliest I think conception is plausible, I think I'll be more like 6w3 days. I told them I was worried it'd be too soon and she said "if" the doc wants to try a scan that hb shows after 5w. Reading mixed things online. If they refuse to scan or worse, scan and don't find it and say YET, it's gonna be a long long long time till our next appointment. Anyone wanna reassure me?