> But it is meaningless since they did not write about it not they stablished commerce
Depends on what you find meaningful! There was almost certainly exchange of goods between Polynesians and South Americans. The presence of early sweet potato agriculture in Polynesia and genetic admixture in both regions points to non-trivial contact. There are even parallels in terms of folk-tales [0]! (Though these are likely older events, more to do with ancient dispersal).
There are also possibly earlier relationships across the Pacific, but these would have been ancient and interesting largely from historical curiousity [1].
[0]https://link.springer.com/chapter/10.1007/978-3-319-39445-9_...