Hyundai charges a subscription fee for remote start built into their cars. First three years are free, paid subscription thereafter. You have to use their app to remote start. There's no button on the key fob.
I know my Kia fob doesn't have a remote start _button_ on it, but if I press lock then trunk, it activates remote start. Perhaps that's an option on Hyundai fobs? After all, Kia is owned by Hyundai.