We have seen from other attempted TLs from other countries the constraints that exist on building large navies. France was limited by a lack of good ports and the presence of England along much of it's coast. As was Germany and the Netherlands. Wheras England (and later Great Britain) had unrestricted access to the Atlantic on one side pulling them towards a strong navy and a peculiar economy that centered around manufacturing woolens for the rest of Northern Europe freezing it's butt off in the Little Ice Age, thereby resulting in sheep forcing farmers off their land pushing England on the other hand pushing England.
Scandinavia also was pushed, in this case, by the Little Ice Age causing repeated famines and crop failures (think Finland 1799) but because Scandinavia was divided between Sweden and a highly conservative and feudalistic Denmark that ruled Norway with an iron hand and tied Danes and Norwegians to their land, Swedes when they weren't starving quietly were expending their energies in futile wars against numerically stronger European powers such as the Holy Roman Empire, Poland, Prussia and Russia.
So the sooner Sweden can unify the Scandinavian Peninsula and build a navy that focuses outward rather than inward toward the Baltic, the stronger a navy Sweden can have,
So the best outcome is for Gustavus Vasa to win the Norwegian Lords to his side alongside the Swedish Lords in 1527 and maybe even take over the Union of Kalmar, lock stock and Denmark.
Failing that, Eric (XIV?) or Gustavus Adolphus are smart enough to concentrate on the easiest parts of Norway to conquer--Norrland, Tromso and Finnmark (Tromso, Bodo, Mo, Mosjoen and Namsos), then Trondelag. Having those ports will give Sweden the outlet onto the Norwegian Sea that it needs to build a navy and a naval tradition to compete with Great Britain. Somewhere along the line, Sweden can take Andalsenes and Romsdalen and work it's way south to Sognefjord, which almost bisects Norway over the course of the 17th Century. These ports can prosper and become Sweden's Liverpool and Bristol and Carlisle and Portsmouth. Sweden has the tall trees needed for tall ship's masts and plenty of wood to manufacture ships.
The longer Sweden waits, the more Sweden will be outpaced by other nations and the more Sweden will become used to stagnating and being small as in OTL. Actions Sweden takes toward developing a large navy will have far more impact in the 16th Century than in the 17th Century and in the 17th Century more than the 18th Century and the 18th Century more than the 19th Century, as with Great Britain.
And leave us not forget. If Sweden can act in the 16th Century and expand east into the Barents Sea, even if Sweden does not stay there, Sweden will encounter the Pomor--seafaring Russians whom the tsars will more or less exterminate in the 17th Century OTL out of fear that they will trade illicitly with Western Europeans. (Sort of a more successful version of the Manchu coastal depopulation policy against the Southern Ming in Taiwan at the same time). Those Pomor have invaluable skills in things like building koch boats that can navigate ice choked waters in places like Hudson's Bay and reindeer herding and fur trading that the Swedes will find critical if they decide to use one of their biggest assets in building a New World Empire--their greater ability to live and prosper in colder climates than any other seafaring Europeans. Swedes and Pomors together can claim and prosper in Newfoundland and Labrador and Hudson's Bay and work their way both inland and along the Northwest Passage, hundreds of years before Roald Amundsen IOTL despite the Little Ice Age. And hang onto "Svensylvania".