The best person to ask would be a doctor.
We are not doctors we are a community of people living with and treating our own illness of hep c. We offer support and advice to our fellow sufferers. We cannot diagnose any medical condition. We are not medical statisticians and we do not have data on every possible situation imaginable nor does anyone.
But as hep c is not easy to transmit in the first place, and if a person was newly infected in the last 7 days which is a big if as the person would not even know they were infected. But anyway they would have a very, very, very, low viral load making something difficult to transmit even that much less of a probability. Perhaps if you could explain more about the circumstances.
Hep c requires the blood of a hep c infected person to come into contact with the blood stream of an uninfected person did something like this occur?
Why do you believe a person was infected for a week and possible infected another person at that time frame?
RNA can often be found in the blood within a week of exposure. The answer to your question is yes, it can be transmitted a week after exposure.