There is no simple answer to this. There was no generally accepted view about the questions (and it really was multiple questions) that Darwin’s book was concerned with. As DrCube says, Lamark’s evolutionary theory was around, but it was not very widely accepted (and it differed from Darwin’s theory in far more profound ways than the difference between natural selection and inheritance of acquired characteristics). Other much vaguer evolutionary theories were also around, such as those of Erasmus Darwin and Robert Chambers, but in many ways these had more to do with political ideas and hopes about the inevitability of progress than with biology as such. Some influential thinkers, such as Darwin’s mentor, Lyell, held that held that life adapted itself to current, local environmental circumstances, but did not see this as an ongoing process of change, and had little or nothing to say about how such adaptation might occur (Lyell’s principal concern was with geology, anyway).
One thing that it is important to realize, however, is that there were no determinedly closed-minded creationists of the sort we have around today. Modern creationism, and the Biblical literalism that go along with it, arose in the 20th century as a reaction against evolutionary theory (or, really, as a reaction against social changes that creationists are inclined to blame, largely but not entirely falsely, on the rise of evolutionism in science). No doubt, before Darwin, if you had asked most people where all the different species of animals and plants in the world had come from they would have said that they were each created by God, but was mainly simply because no-one really had any better answer to offer at that time. It was certainly not because most people believed that the creation story in the book of Genesis must be literally true. Few if any Christians in the 19th century thought like that, and, in fact, that had not been Church teaching since at least the 5th century AD, if ever. There was some resistance, on religious grounds, to Darwin’s ideas when they first appeared, but this was not rooted in Biblical literalism, and for the most part it collapsed fairly quickly. Within a decade or so of the publication of The Origin, both the Anglican and Catholic churches (and probably most other Christian denominations too) had reconciled themselves to the truth of Darwinian evolution.
Another thing to remember is that in The Origin Darwin is not just concerned to establish natural selection as the mechanism of evolution. Before that, and more fundamentally than that, he must establish that evolution is a process of differentiation over time, so that different species arise by differentiating themselves from parent species. This was a much more significant “missing ingredient” from earlier ideas about evolution than teh idea of natural selection was. The evolutionists before Darwin had not understood that evolution proceeds by differentiation, and Lamark’s theory, in particular, is directly incompatible with it. Lamark thought that each species had originally arisen individually, in some primitive form, out of non-living matter (whether through “spontaneous generation” or through creation by God is not really to the point for him) and had then evolved over time to reach its present, less primitive form. Human beings, according to Lamark, are not descended from apes or monkeys. Rather, the human species, and each species of ape and monkey, arose separately, starting as some form of microbe or invertebrate and gradually evolving into its present form. Present invertebrates are still invertebrates because their species did not arise from non-living matter so very long ago, and has not had much time to evolve into a more complex form. He thought the human species, by contrast, must have first arisen very long ago, and thus has had a very long time to evolve from it original primitive invertebrate form to its current state of complexity and sophistication.
Darwin’s realization that evolution does not work like this, but by differentiation (and extinction) is distinct from, and, I would venture to say, more profound and revolutionary, and more basic to modern biology, than his discovery of natural selection as the mechanism by which this occurs. We know from his own private notebooks that he first came to the idea of evolution by differentiation, and became convinced of its truth, soon after he returned from his voyage on the Beagle, and he then set out very deliberately to try and discover a mechanism that could bring this about. That took him several more years of quite focused research. What is more, through the rest of his life he was much more strongly committed to the idea of evolution by differentiation than to that of natural selection. In the later 19th century, some fairly serious scientific objections to the theory of natural selection were raised (they were based in math and physics, and not at all in religion), and Darwin took these seriously to the extent that, in later editions of The Origin he somewhat downplayed the importance of natural selection, and allowed for the possibility of other mechanisms (including ones deriving from Lamark’s ideas) through which species might differentiate into different descendant species. What he did not retreat on at all, however, was the more basic insight that evolution is a process of differentiation over time. (The math and physics based objections to natural selection were refuted in the early 20th century, by discoveries about the mechanisms of genetics and by the discovery of radioactivity, and it was realized that Darwin had been essentially right in the first place.)
The point is that much of The Origin of Species is concerned with making clear the idea of evolution as differentiation, and with convincing the reader that the known facts of biology only make sense if present day species (and the known extinct fossil ones) and their distribution around the world actually arose in that way. It is only secondarily concerned with convincing you that the mechanism that brought about that differentiation was natural selection.
Incidentally, it might be worth checking which of the original editions of The Origin the copy you are reading is based upon. I think there were something like eight editions in Darwin’s lifetime, and he did quite a bit of re-writing. As I said, the later editions actually play down the importance of natural selection as compared to the earlier ones. There are probably other changes between earlier and later editions that may be considered improvements, but as far as natural selection goes, Darwin’s view of it in the earlier editions is more in line with current science than what you will find in the later ones.