How do you know your partner doesn’t already have it? Most people who have HSV one, have no symptoms. If you just had your first outbreak, unless you have engaged in oral sex performed on you (the cause of HSV1 on the genitals) with someone else, your current partner would be the source.
Even if your boyfriend has been tested for HSV1 specifically, IgG tests for the strain can miss up to 30% of infections.
Transmission during sex/oral theoretically can happen but unlikely. HSV1 genitally sheds infrequently.