Actually, the "Singapore was a third world fishing village" trope is mostly PAP propaganda. Singapore was very successful economically before WW2, and ranked second behind Tokyo or Shanghai as the wealthiest city in Asia by most measures.
Singapore was a British colony before WWII, not a nation state though. All the Straits Settlements accumulated that wealth on the back of colonial England, and before that it was part of the Johor Sultanate but was just some jungle that no one cared about, not even the Sultan himself who gave it to the British.
After leaving Malaysia it ranked right down the bottom on basically every economic and social measure, unemployment was at 10% and many lived in slums. Plenty of third world countries had better GDP per capita numbers.
Also my estimates are just fine according to that clickbaity link and a minute of research:
Upfront:
$10 tender application
$39 three year hawker license
$321 Basic Food Hygiene Course
$260 Stainless steel cart + delivery From JB [1]
Ongoing:
$49 a month for a stall at Mei Chin Road
$600 a month in cleaning/service fees
$1000 a month in raw materials for say 100 chickens + everything else. Serves 1000 dishes.
It's certainly possible. That rental isn't common but certainly not out of the ordinary, you can get cooking stalls for ridiculously cheap.
Also, you're off by a factor of around 20x on your estimate of the costs of setting up a hawker stall: https://blog.seedly.sg/how-much-to-be-hawker-singapore/