Their home destroyed, the family learnt to survive as best they could without electricity or running water.
"I was very poor and we were moving, moving, moving," she said in broken English. "It was a very difficult time."
Although her height — which comes from a hormonal imbalance that caused her to continue growing into her twenties — was immediately apparent, her sporting experience was limited to launching a shot put as far as she could.
Faced with people staring and making cruel taunts, she shrunk into herself. It is still evident in her demeanour today — her cheery, kind face belying her introverted nature.
Only when she moved to study economics at university on Sri Lanka's east coast did she step on to a netball court for the first time.
She was soon brought into the national set-up and relocated to Colombo, where she was tasked with learning Sinhalese to converse with new teammates.
It was in her new job at Seylan Bank in the capital that she met Thilaka Jinadasa, now in her second stint as Sri Lanka's coach.
"When she first came to Colombo, she didn't speak Sinhalese," said Jinadasa. "Just imagine how hard it must have been for her. She was very shy and didn't want to do any strength work because she had this extraordinary height so she didn't think she could fit into any of the machines. I told her I could organise it for her, so she started believing in me and following me.
"When she came to the 2005 Asian Championships, she was on the bench because she was very slow. I intended to give her confidence, to show her she just needs intelligence on the court."
It sounds simple enough, but Sivalingam was being asked to learn the type of netball basics most girls are taught at school: how to move, where to stand, how to land correctly.
"She had never played netball, so she didn't have that skill," said Jinadasa. "Sometimes she still makes basic errors because of that."
Her physical advantages were enough to overcome her lack of experience. At the 2011 World Cup, she scored 290 of her 296 shots — a ludicrous 98 per cent accuracy.
Yet by 2015, a new coaching regime had bizarrely cast her aside.
"Administration problems," says Sivalingam, by way of simple explanation. Sri Lanka finished last in her absence.
Unwanted by her national side, she became her country's first professional player when offered a contract to play in Australia's state netball league — the third tier of the sport — for City West Falcons, Victoria's most successful team.
She has now spent three years there, boarding with her coach and former Commonwealth Games champion Nicole Richardson, while developing her game into her late thirties and early forties.
When Jinadasa was reappointed at the Sri Lankan helm last year, she had no hesitation in bringing back her star shooter. Sivalingam's ambitions in what she confirms will be her last World Cup remain as lofty as ever.
"I want to be the best shooter in the world again."
