While we know very little about general public perception of the Southland, we do know that the academic consensus among geographers was that there was a vast new land awaiting discovery in the southern hemisphere, and that it was potentially extremely rich.

To cut a very long story short, most geographers assumed, from their reading of Ptolemy, that earth's southern hemisphere would contain a landmass equal in size to Eurasia and the known parts of Africa. It was assumed there would be a "balance" in this regard between the northern and southern hemispheres. So the expectation was that there would be a discovery of a much larger, richer and more varied landmass than Australia.

In addition, thanks to Mercator's misreading of Marco Polo, it was widely believed that some parts of this new Southland were already in contact with various Asian states and were known to offer rich potential for trade and conquest. Three of these imagined "provinces" can be seen marked on contemporary globes - Lucach, Maletur and Beach. They were understood to be sources of gold and spices – so the expectation was that exploration and discovery would be worthwhile. At one point the Spanish government in Chile even appointed one of the Conquistadors there as "Governor of Beach", anticipating a discovery and, presumably, a successful invasion and the acquisition of these new territories.

Sources:

Miriam Estensen, Terra Australis Incognita: The Spanish Quest for the Mysterious Great South Land

Alfred Hyatt, Christopher Wortham et al [eds], European Perceptions of Terra Australis

Günter Schilder, Australia Unveiled