Go back to Vinland, basically. There's a basis for this, like how Didrik Pining was hired to explore Greenland to see what happened to the locals there. Start with propping up the survivors of the Greenland in the late 15th century, then go to Vinland proper and exploit its rich cod fishing grounds. By the early 16th century, start up the fur trade amongst the local Algonquians to undercut any rivals (like Russia). Since at this point OTL we have the Kalmar Union in place, we can help Sweden out by giving them rights to colonial settlements perhaps populated by Forest Finns, who like in Scandinavia or in New Sweden OTL, carve out a new homeland from the forest. The Finns are very hardy settlers, and if Scandinavia needs to compete with the British, will make a perfect counterpart to New Englanders (preserving the Finnish language ala Canadian Gaelic would be interesting, and perhaps likely to occur in more isolated places like Cape Breton Island). Additional money for their empire can be raised in the Caribbean and Africa, where no doubt the Kalmar Union can maintain some slave castles to import plenty of slaves for their sugar plantations to make income for their colonial empire. As for the Baltic, we can still have wars there, we just need to keep the Swedes from seceding and ideally conquer Karelia, Ingria, and Livonia. The main enemies in that theater--Poland, Lithuania, and Russia--are unlikely to present much of a challenge to the colonial empire, but as long as the Swedes can get something from this colonial empire, they'll use that income to help Denmark-Norway out in protecting the Baltic.
This is best-case scenario, but a "return to Vinland" may be possible for Denmark-Norway alone. But ideally I'd combine a core of Forest Finn settlers (i.e. New Sweden) and a Danish-Norwegian "return to Vinland". At worst this leads to a "New France" situation where Britain conquers them before long, at best it could be that our Vinland extends as far south as the Ohio and Missouri and thus becomes one of the great powers along the lines of the United States.
The main problem is that for North America, Scandinavia will need a big navy to compete with the British/French/Spanish, which means they need some good international alliances. An oceangoing navy is separate from the fleet in the Baltic they need to compete with the Polish or Russians. Ideally, maybe have a few puppet states in North Germany like Bremen, Mecklenburg, and Oldenburg, keep Livonia in personal union, add Ingria and Karelia to Finland, and have Baltic territorial goals limited to keeping Poland, Lithuania, and the Russians weak. As for Germany, keep the puppet states secure and as buffer states against potential rivals. And elsewhere, build a strong navy whose goal is to establish superiority in the New World and Africa.
As I noted, Denmark-Norway or OTL Sweden can do something similar, but it's much easier if the Kalmar Union (or another union of Scandinavian crowns, maybe under a wanked Sweden) can succeed and put together this empire.