Stromatolites as a lifeform have been on Earth over 3 billion years? How does the faint young Sun hypothesis cast doubt on this dating and standard chronology?

They may look like round rocks, but they’re alive. Moreover, they are modern versions of one of the oldest known forms of life: stromatolites. Fossils indicate that stromatolites appeared on Earth about 3.7 billion years ago – even before many of the familiar stars in the modern night sky were formed. In the featured image taken in Western Australia, only the ancient central arch of our Milky Way Galaxy formed earlier. Even the Magellanic Clouds, satellite galaxies of our Milky Way and visible in the featured image below the Milky Way’s arch, didn’t exist in their current form when stromatolites first grew on Earth.

Stromatolites are accreting biofilms of billions of microorganisms that can slowly move toward light. Using this light to liberate oxygen into the air, ancient stromatolites helped make Earth hospitable to other life forms including, eventually, humans.
Ancients of Sea and Sky | NASA


Faint young Sun problems for stromatolites?

When the Earth was born 4.55 billion years ago, the Sun should have been about 30 per cent fainter. Our planet should have been frozen solid. However, evidence contradicts this. Geologists have found ancient rocks that could have formed only in the presence of liquid water.

And biologists have found fossil bacterial colonies called stromatolites from about 3.5 billion years ago. Like their modern counterparts off the coast of Western Australia, they lived in shallow coastal water.

The fact that the youthful Sun was too feeble to prevent the young Earth from freezing yet the young Earth evidently did not freeze is called the faint young Sun paradox. It was first recognised as a puzzle in 1972 by the astronomers George Mullen and Carl Sagan.
When our sun was young | New Humanist

Early in Earth’s history, the Sun’s output would have been only 70 percent as intense as it is during the modern epoch. In the environmental conditions existing at that time, this solar output would have been insufficient to maintain a liquid ocean. According to the Standard Solar Model, stars similar to the Sun should gradually brighten over their main sequence lifetime due to contraction of the stellar core caused by fusion. However, with the predicted solar luminosity 4 billion (4 × 109) years ago and with greenhouse gas concentrations the same as are current for the modern Earth, any liquid water exposed to the surface would freeze… and the basic carbon isotopy is very much in line with what is found today.
Early solar output – Faint young Sun paradox | wikipedia