There is this closed Facebook group called Single Parents Singapore (SPSG). Perhaps you can request to join the group and see if they have meet ups or gatherings you can go to socialize, make friends and stuff. I have a few single moms friends who seem to have put dating on hold to concentrate on their child and career. Usually it's (pesky) friends like me and a few others who'd try to matchmake them with nice guys we know. Since you don't have a large network of friends yet, perhaps you can start from there -- I always find that meeting people through friends are easier because there's already an "in-built filter".
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