Three pieces of information are very important data regarding your question: “Does your girlfriend have regular periods?”; “When did she expect her next period if she had regular periods?”, and “Did she take a home pregnancy test because she had missed her period?”. You could be the father if the duration of her menstrual cycle is somewhere between 38-40 days. In that case, her next period could be expected around the 26-28th of July; ovulation would occur around the 14th of July. A pregnancy test can be accurately positive 5 days before an expected menstruation has been missed (23rd of July) if there was conception. This scenario is certainly possible... but not common. It seems that there is reason to be suspicious about your paternity. If your girlfriend took a pregnancy test after she had already missed her expected period then you cannot be the father. A DNA-test can accuartely and definitely solve the mystery.