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I believe the term spontaneous generation concerns the very first organism from which every other organism supposedly evolved

Sure. Look at the last word in the sentence. It is no part of the theory of evolution to postulate how living cells came about. Evolution simply describes how living cells evolved after they arose. There are theories which postulate how cells arose, but they're at the moment highly speculative, with no substantial experimental or observational data.

Fair enough. But consider this: following the theory of evolution backwards, one must necessarily arrive at the existence of a first organism. Since Evolution, when not coupled with intelligent design as some do, promotes the idea of random changes (mutations) causing eventual macroscopic changes in an entire species, then it would also have to promote the notion that a random chain of events created the first organism (spontaneous generation). That MUST be part of the theory. It would be silly for a proponent of evolution to say that the first organism was created by an intelligence, but then all of the subsequent occurrences were random, devoid of intelligent influence. Therefore, while modern evolutionary theory may not explicitly include the concept of spontaneous generation, it is an implied and necessary part of the theory, unless you couple it with intelligent design.