1605 was the first Danish expedition to reestablish contact with the Norse settlements in Greenland. In OTL, there was a 1619 Danish expedition to find the Northwest passage. I vaguely thought of a early Danish trip to OTL Hudson Bay just to give them a head start.
Since in 1607 the Virginia Company founded Jamestown and in 1608 Champlain founded Quebec, this is an interesting decade. Having the Danish succeed and the English and French fail (at this date) might go a long way. The French they will try again later, perhaps elsewhere. In England, King James was very interested in good relations with Spain, so if Virginia fails, he might prohibit further attempts in the New World.
Russia: In 1648 Semyon Dezhnev sailed as the first European through Bering Strait found Alaska and established an ostrog (fort) at the Anadyr River. But he was more or less forgotten. A hypothetical direct follow up would have been more or less led by individual cossack leaders, not by the Russian state, but once report of gold arrives in Moscow, that might change. So the TL might have a Russian-American company more than 100 years earlier.
New Sweden is very iffy. In OTL, it was the idea of Peter Minuit, a disgruntled employee of the Dutch WIC, who managed to convince the Swedish government to found a colony in an area the Dutch had claimed already. As soon as anything is changed in the previous years, New Sweden will probably vanish.