Not sure about the Next World. However Jews don’t proselytise to non-Jews because they lived pretty much as guests in the land of others. If they had been proselytizing, they could have been evicted.
Also, non-Jews don’t need to follow the 613 mitzvot. Instead they just have to follow 7 Noahide laws.
Prohibition of Idolatry
Prohibition of Murder
Prohibition of Theft
Prohibition of Sexual immorality
Prohibition of Blasphemy
Prohibition of eating flesh taken from an animal while it is still alive
Establishment of courts of law