You can get the 37 pop city, your main constraint is happiness, are you only going with 1 city, if you have an empire can you afford a 37 pop city worth of unhappiness, you have lots of other cities to cater for.
But as for food, farms give an additional +2 to +4 food depending on tech, maritime city states give extra food, social policies give extra food, social policies can make your population & specialist population eat less food, buildings can give food directly, basically theirs a whole lot of stuff you can do to increase your food in take, so can you build a city capable of working all of its tiles, and probably keep growing and have more specialists, yup.
Also don't forget the health mechanic no longer exists, so its even easier to keep a city growing and growing. I believe theirs even a social policy that allows your capital city (which you would assumeably be the first city you want maximised with 37 pop) to grow faster.
Indeed, it will be possible.