Judaism most certainly does believe in reward and punishment. The Jewish Bible is full of reminders of the rewards for those who do good, and the punishments for those who do bad. So the short answer is that I chose to gamble away my beloved cheeseburgers and Saturday tv shows on the chance of getting into heaven.
Longer answer:
Judaism applies the above to both Jews and non-Jews. The difference is that God has different expectations from the two groups. For example, God expects non-Jews to avoid murder and killing etc., but Jews also have a number of rituals and holidays to follow. (Lots of other differences too.)
Jews don’t actively convert non-Jews because there’s no need to. As long as the non-Jew is doing those few things that God expects, there’s no need to burden them with all the extra stuff, and they’ll get the afterlife reward that they’ve worked for. OTOH, if a non-Jew sincerely wants to join the Jewish people, we welcome them.