How do we know that the continents were formed during the Precambrian?
Evidence from radiometric dating, especially of zircons.
The Earth's major continents are made up of stable bodies of rock called cratons. These cratons are incredibly ancient - most of them are over a billion years old! That is well back in the Precambrian Period.
We know this because of radiometric techniques like potassium-argon dating. These techniques rely on known rates of radioactive decay in rocks. Certain isotopes of elements like uranium and thorium decay into other elements at a known rate. By comparing the proportions of the original isotope and the decay product in a rock, we can estimate how old that rock is.
Of course, rocks are recycled over time due to the processes in the rock cycle. You need really tough, resistant mineral grains to preserve radiometric data from Precambrian times. Zircons are an example - they are resistant to both physical and chemical weathering. Some zircons found in Australia have been dated to 4.4 billion years ago - so the land they were found in is almost as old as the Earth itself!
Zircons found in all the major continents provide evidence that the cratons they're made of are Precambrian in age, through radiometric dating.