The Isua Greenstone Belt (IGB) is dated at 3.7 Ga, so there are several hundred million years in that "immediately."

So, what the hell is a Greenstone Belt, anyway? It is a regionally extensive series of rocks that have been subjected to moderate pressure and temperature metamorphism, known as "greenschist." Here's a graph:

https://upload.wikimedia.org/wikipedia/commons/f/fe/Metamorphic_Facies.jpg0

I've done a fair amount of work in the greenschist rocks of the Southwest United States and while they are a full billion years younger than those in Greenland, the metamorphism is similar. Here's the thing about interpreting metamorphic rocks, even those of the greenshist facies, you have to assume they are not what they used to be. And greenstones are weird.

Within a greenstone belt, the deformation of the rock can vary greatly, even if they were subjected to the same pressure and temperature conditions. This makes interpreting original textures in the deformed rock challenging. Furthermore, the tight folding of rocks in greenstone belts results in some rather interesting structures. We had a saying in the field: "the rocks are so F'd up they look normal." Look, I could go on about psuedo-structures in transposed isoclinally folded lithologies, both micro and marco, for hours - days, really - but I'll spare you. Basically, we need to be very careful of classifying original sedimentary structures in greenschist facies metamorphic rocks.

That being said, they could be stromatalites.