Katchen
The Swedes might not have been able to settle Ingermania during the 1630s. But they were able to make a good start at colonizing Norrland. I believe Lulea and Umea were founded about that time.
Which brings us to the New World. I suspect that the biggest problem New Sweden had was that it was in the wrong place, sandwiched between Dutch and British colonies. It had very little future, even if it got going. The British would simply take it over in 1675 when the Swedes lose a war to England and the Netherlands.
But if the Swedes were to found a New Finland (because the terrain is all swamp--fens,) in Hudson's Bay, with trading posts at the mouths of the Albany, Nelson and Churchill Rivers and at Chesterfield Inlet, as well as on Hudson's Bay's east coast, such an enterprise would yield enough pelts in trade to be immediately profitable and compete head to head with Russia's fur monopoly. And yes, Finns and Lapps would be quick to travel to "New Finland, especially if some way could be found to ship domesticated reindeer to enable Lapps to build herds (wild caribou won't work). And Gustavus Adolphus could appropriate a prize for the first Swede or Finn to find a route across North America from Hudson's Bay to the Pacific Ocean. The prize would be claimed within 50 years. And much sooner than that, Swedish explorers would beat the French to the Gulf of Mexico down the Mississippi River from Lake Winnipeg and either the Winnipeg or the Red River of the North to the Minnesota Rivers and perhaps even Lake Superior via the Albany River (which would obviously be called something else). and Lake Nipigon. The Swedes have one thing going for them in the colonial sweepstakes. They may not have a large population at first and they keep getting into wars they don't win but they know how to live and prosper in climates that are too cold for other Europeans. And from Hudson's Bay, they can access the North American Great Plains where they can grow a lot of graain, building locks on the Nelson, Albany and Churchill Rivers and perhaps canals, before railroads are developed to create a river route along the Churchill, Reindeer, River to Cochrane Lake to Lake Athabasca to the Pe3ac River portaging to the Upper Fraser and Nechako and thence to the Skeena and the Pacific by the early 18th Century. The Orcadians (Orkney Islanders) who worked for Hudson's Bay Company didi it. Surely Swedes and Finns can do it.
And yes, down the line, once the Swedes have reached the Pacific but must communicate with it by sea, they can settle Patagonia the same way.Only the Russians are equally cold adapted.