Which part of the iron age would you like them introduced?
The further back you go, the higher the solanine levels. The Tawantinsuyu began cultivating potatoes from 200 Before Counter. Although they were consumed before then too. Villagers would take their potato harvests to mountaintops, where the potatoes were left overnight to freeze. Next day, the villagers would return to their harvests, bring them down from the mountains, spread them out in the sun and step on them to break the potato skins. The breaking of the skins and thawing process ruptures the cell walls, allowing water to escape and carry away the toxic solanine. The process was usually repeated over 3 successive nights.
Centuries of breeding and cultivation led to less toxic varieties which the OTL Spanish found. Originally early potatoes in Europe were used for animal feed. It took a little while for them to become a popular crop. You also have the issue of how many varieties are you introducing? Without sufficient varieties, the potato crops will be susceptible to disease. Which was the cause of some early potato related famines in Europe. Later somebody bred a potato hybrid which was resilient to disease.
So if you would like a much earlier introduction of potato. Whoever gets them to Europe HAS to know the Tawantinsuyu cultivation and freeze drying methods to remove the solanine. Which means some sort of contact, maybe via trade. With the right PODs I guess you could have a spice trade analog develop between the Tawantinsuyu and classical Mayans, and then go from there. Or alternatively have a maritime civilization island hop across the south pacific. If they're lucky enough, they make first contact with the Tawantinsuyu and begin trade. Perhaps the maritime civilization views the potato as something worth trading for, and takes them back. Introducing them to China and India, and from there they spread west until they eventually reach Europe.
Alternatively, have trade contact between the Tawantinsuyu and Maya. So potatoes reach the Caribbean shore, then perhaps a maritime civilization like Qart-Hadash (Carthage) makes an accidental discovery. Maybe after a ship gets blown off coarse. Or with sufficient advances in ship building, a wealthy sailor feels adventurous and sails west on a whim.
Consequences for Europe really depend on how fast they can produce a hybrid potato more resistant to disease, and how well the populations accept it. If you can get an early potato hybrid and everybody loves them, they will do well. Which means a higher population. The high nutritional value of potatoes means stronger resistance to diseases like tuberculosis and measles. So again, that's great for those eating them.