The requirement comes from section 142 of the Companies Act 1967: a company must have a registered office in Singapore from the date it is incorporated.
That produces a sequence which catches out most first-time founders — and every founder incorporating from overseas. The address is a required field in the incorporation filing itself, so it has to exist, and you have to be entitled to use it, before the company does.
Secure the address
You need a physical Singapore address you are entitled to use, before anything is filed.
File the incorporation
The registered office address is a required field in the BizFile incorporation form.
The company exists
Only now does the entity — and its UEN — come into being.