Hello,
Thank you for asking the query.

Very less likely. I would say near impossible or something like only a text book possibility.

There are many road blocks in the transmission of virus in this scenario:

1. A typical kiss in the cheek might not transmit the virus to the person. And transmission would only happen if the affected person is actively shedding virus.
2. The partner (girlfriend) already had cold sores – That means some level of protective anti bodies are there in her system. This could offer protection again further HSV 1 infection
3. HSV1 is less likely to cause genital infection.

Putting all these together, it is very less likely that the infection has been transmitted.

Hope this helps. Please feel free to ask follow-up question. Thank you .