The crisis broke in mid-September, a month after the Olympics, but several Chinese reporters had long known about babies being hospitalised after drinking tainted milk, yet were muzzled by the authorities, the critics say.
An editor at a respected southern China newspaper said that as early as July one of his reporters was investigating how milk powder might have been to blame for children developing kidney stones and falling seriously sick.
"As a news editor, I was deeply concerned because I sensed that this was going to be a huge public health disaster," Southern Weekend news editor Fu Jianfeng said on his blog.
"But I could not send any reporters out to investigate. Therefore, I harboured a deep sense of guilt and defeat at the time."
Fu's blog posting was later removed, although it could be read on some overseas Chinese websites. Fu himself could not be reached for comment.
An estimated 53,000 Chinese children have been sickened after the industrial chemical melamine was added to milk products, and four infants have died.
The first of the baby deaths was on May 1, more than four months before the scandal went public.
Starting with Sanlu milk powder, the scare has gone on to envelop numerous Chinese firms and international companies operating in China, including global giants Cadbury and Unilever.
Chinese premier Wen Jiabao vowed over the weekend to work to restore his country's reputation, saying it was facing the problem "candidly".
However, there are claims that Chinese authorities reverted to the familiar practice of squashing the negative news reports, apparently conscious of the damage it would do to the August 8-24 Olympics.
"Several Chinese journalists have said it is becoming more and more obvious that the authorities in July prevented an investigation into the toxic milk coming out so as not to tarnish China's image before the Olympics," said a statement by media rights group Reporters Without Borders.
Sanlu Group began receiving complaints of sick children as early as last December, a recent cabinet probe found in an apparent attempt to shift the blame for the delay.
It also said Communist officials in the northern city of Shijiazhuang, where Sanlu is based, delayed referring the matter to higher authorities for more than a month after Sanlu finally told them of the problem on August 2, six days before the Beijing Games began.
"It is a concern that the first cases appeared early, but were concealed during the Olympics. A perfect environment was needed for the Games," said a Western product-safety expert who asked not to be named.
Despite the World Health Organisation and United Nations raising concerns about the delay in exposing the risks, rights groups say the Chinese government is continuing to silence reporters, suppressing media coverage vital to determining blame and preventing a recurrence.
"The government's gag order on the media has the effect of shielding those responsible for the tainted milk from accountability," Chinese Human Rights Defenders, a network of domestic and foreign rights activists, said in an emailed report.
It cited several instances of reporting by Chinese media censored or banned by authorities. The instances could not be confirmed by AFP.
The Brussels-based International Federation of Journalists last week also criticised China for "escalated restrictions" on reporting on the scandal.
It said propaganda authorities had expelled journalists from at least four Chinese newspapers in the same city as Sanlu's headquarters.
It also said authorities had deleted articles on the case from news websites and insisted on pre-approving related articles.
"China's Central Propaganda Department's attempts to control the media's reporting of a very serious public health crisis can only serve to heighten fears," the IFJ said.
"A free flow of information through a free media is vital where lives are at stake, and government restrictions on journalists may be endangering public health."
China has blamed the scandal largely on milk brokers adding melamine to boost milk protein readings.