Depends if you count Russia as a European country, they set up colonies in Alaska in the 18th century. The Ottomans might have been looking to create a colony there as their navy visited the colony in 1616 according to this source https://www.dzkk.tsk.tr/data/icerik/371/7_Atlantikte_Turk_Denizciligi.pdf which I unfortunately can't find an English translation.