Unless there is a carryover from a previous session, the first person chosen for the hot seat in a new session is the first person to answer the first question correctly.
After that, the person who answers the questions correctly faster than everyone else in the audience is the one chosen for the hotseat. Of course, the person in the hot seat has to miss a question before anyone gets there. Sometimes you have to answr a lot of questions correctly very quickly to be the one. Sometimes you end up next to be chosen (they show the seat numbers of the 10 fastest) but the buzzer sounds before anyone misses or the person misses a question too late for someone to start over. Each session starts over again.
Best wishes -