How Can I Confirm The Paternity Of The Pregnancy And The Date Of Conception?

Hi, I have a question about pregnancy. My last period began on the 19th of April. I have had only one partner since the 7th of April but had a one night stand a week before this new relationship, on April 1. On the 24th of May I tested positive for being pregnant. I am worried that I can’t be sure this belongs to my new partner and what I read online is confusing. I really hope it is but need a professional to help me please. Thank you.