"first proposed that" is grammatically correct and can be used in written English.
It is typically used when discussing a proposal or idea that was suggested or put forward before any other ideas or proposals. Example: The committee first proposed that we implement a new recycling program in the office, which was later approved by the majority of employees.
A year ago, when he first proposed that Republicans turn the page he drew sharp criticism from Rush Limbaugh, among others.
When Beard first proposed that idea in the 1990s, he was "completely ridiculed," he recalls.
The computer company first proposed that Microsoft write the BASIC interpreter.
It was Élie Metchnikoff who first proposed that "aging is the replacement of noble elements by ignoble ones" [ 1].
Ohno (1970) first proposed that gene or genome duplication is a major mechanism for generating functional innovation and genome evolution.
We first proposed that hMYH is the unknown factor involved in accumulation of hTopBP1 onto DNA lesion for inducing the interaction between hRad9 and hTopBP1.
In October 2011, the Dutch oil and gas firm Shell first proposed that a sole greenhouse gas target take the place of policies that also supported renewables.
The baboon expert Clifford Jolly first proposed that our ancient relatives were joined together by a baboon-like web of connections.
In 1912, when Alfred Wegener, a German meteorologist, first proposed that the earth's continents were moving around, the notion was ridiculed.
"It isn't often that an institution gets the chance to correct for a previous error," said Lucius Outlaw, Vanderbilt's associate provost for undergraduate education, who first proposed that Mr. Lawson be asked here for the year.
Its modern roots lie in the Enlightenment, when it was first proposed that good design of the built environment could do more for public health than the medical profession could.
