Marsupials are found in North America and Australia, but they would not have been able to swim across the ocean. According to scientists, how did this group of organisms come to live on two separate continents?

Marsupials used to have adaptations that allowed them to swim but lost these adaptations over time.
The two groups of marsupials evolved independently of one another on two separate continents.
The continents were once connected, and marsupials were able to migrate over the land.
The oceans were shallow in prehistoric times, which allowed the marsupials to travel from one continent to another.

The continents were once connected, and marsupials were able to migrate over the land.

Well of course they could once walk between North America and Asia, but perhaps had to wade here and there from South Asia to Australia through the island chain.

Yes, that is also a possibility. The land bridges that connected the continents may have been partially submerged at times, requiring marsupials to swim or wade short distances to reach their new destination. This gradual migration over millions of years helped marsupials establish populations on both North America and Australia.