Forgive me for the brevity of this answer, but they did and didn't (though somewhat did not largely pierce the interior of the south American continent)

With regards to Spanish colonization, part of why their empire expanded to the degree that it did was because they essentially "absorbed" already existing native communities and social infastructure from within the inca and Aztec empires and did migrate en masse, to larger degrees than the French and English, in said time period.

Beyond this though, much of the interior remained unpopulated. Look at the modern American South West or California- nominally under Spanish control, but very sparsely populated and remained so, as your post points out and which in part answers your question, until the Americans took it over (though even now, it's still very sparsely populated).

With regards to the Amazon basin, large chunks are still very much unexplored and underpopulated, so it's not inaccurate to say that the Spanish did not expand into that region considerably (in modern day Bolivia, Colombia, and Venezuela), in addition to the Portuguese having defacto claim to most of the Amazon.

In the former Rio de la Plata, much of Patagonia wasn't conquered and occupied till the mid 19th century (almost parallel to the westward expansion period in America).

With regards to Paraguay and Northern Rio de la Plata, where they did pierce the interior, they largely did so due to the river systems present and moderate climate (at least compared to the Amazon). Paraguay, for instance, is largely a country defined by it's Rivers.

So in short, they did and they didn't pierce the interior (in some areas, yes- such as the former Inca or Aztec Empires or Rio de la Plata), but to the degree that the question seems to imply, much of the interior and Amazon remained as sparsely populated as "the West"

Ie, the Amazon, Patagonia, and "the South West" under Spanish control remained very sparsely occupied par to the North American continents occupation by the US, Britain, and France.

To add to this answer, they did establish forts (though usually these were religious settlements) like the French, some of which became later US cities, such as Santa Fe.

Yes, the rainforests did stop colonization somewhat, and Spain and modern Latin America have only just as recently pierced the Amazon,

And while the Inca and Aztec were quite advanced in terms of infrastructure, the Spanish had their own fair share of Natives to deal with in tribes within Patagonia, or the Comanche and Apache in the South-West, for instance.