using credit card to have a nice credit history to buy property sounds like advice for other countries, nothing to do with Singapore where 80% live in public housing. haven't heard of someone denied HDB loan because he doesn't have a credit card
as for private housing... if you have the wealth to buy private housing and you managed to get where you are without a credit card... why bother getting a credit card just to pad your credit score?
Even for SG private housing loans, there are so many differences from US mortgages. All those US states with non-recourse mortgage laws, subprime crash was a disaster waiting to happen.
The fact that you don't have a credit card to pad your credit history in SG is really inconsequential. banks already have well established methods of deciding on private housing loans that don't require you to have a history of paying up credit card debt. Banks are not dumb enough to think that paying a $500 credit card bill on time means you are creditworthy when it comes to a 7-figure housing loan.
Furthermore, you will presumably already have records of having successfully paid up your HDB loan which is probably more important to the bank than paying $500 credit card bill. (if you go straight to private, skip HDB, you won't be here asking for advice....

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