I've read something about the word for sweet potato being the same in Aymara and some Polynesian language... I don't know, if that's the only evidence it seems like a stretch. Is there any solid evidence backing up this claim?
There was actually a recent study proving contact and to me suggests it was the other way round, that a small group of North Andean people made contact and had descendants in Polynesia.
https://www.smithsonianmag.com/science-nature/native-americans-polynesians-meet-180975269/ https://www.nature.com/articles/s41586-020-2487-2
The other pieces of evidence comonly cited are the sweet potato you mentioned and chicken bones. the chicken bones is mostly discredited by modern DNA techniques suggesting they have sparate but related lineages both having the same ancestor population thousands of years ago https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3977275/
The sweet potato theory is cirucmstantial The word for the crop in central Andean and polynesian languages could share a common root word. However it should also be noted that such coincidences do occur for example the word for dog in the Mbabaram language of Australia is also dog pronounced exaclty the same way as English despite no contact. Also a recent genetic study suggests that the polynesian sweet potato broke off from the american version over 100,000 years ago so likely was dispersed by floating on the ocean https://www.cell.com/current-biology/fulltext/S0960-9822(18)30321-X?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS096098221830321X%3Fshowall%3Dtrue
Though that study has been criticised for a very small sample size consisting of one polyneisan plant from Tahiti. I vaguely remember another study suggesting a second introduction whereby polynesian and american sweet potatoes would have been crossed after the above mentioned date by looking at DNA evidence though as i can't seem to find the study take the last part as possibly being me misremembering.
And a potential circumstantial evidence against Polynesian -> South America transit is the lack of the polynesian rat in the Americas which is otherwise found wherever Polynesian peoples went and can be used to track the order islands were settled. https://www.pnas.org/doi/full/10.1073/pnas.0403120101
Of course we can't rule out that e.g. the rat was introduced but quickly went extinct due to increased competition in the Americas or wasn't taken on those particular voyages if they occured.
Edited to add the bit about the pacific rat.