It's almost certain that practically all important innovations have been invented more or less simultaneously by multiple people in different places. The currently prevailing idea among those who study innovations and their history is that new ideas and new technologies (and here the term "technology" is used very loosely, to mean all "means to fulfill a human purpose" to quote Arthur 2009) are always combinations and recombinations of existing physical and mental elements. When these elements become available, it is likely that multiple people will have access to them and thus are able to combine them for the idea. Multiple authors have studied simultaneity in innovation and come to this conclusion; to note just a few besides aforementioned Brian Arthur, Ogburn and Thomas (1922), Brunk (2003) and Lemley (2012).

Simply because early human societies were far less connected than today's society - where simultaneous innovation is still the norm - I believe we can confidently state that people most likely invented the wheel, fire, and even agriculture itself independently, once their material surroundings became conducive to such innovations to be taken into use. For example, there are at least eleven separate locations where agriculture came into use.

Sources

Arthur, B. W. (2009). The Nature of Technology: What it is and how it evolves. New York: Free Press. (BTW I'd very much recommend this book to anyone who's interested in what technologies actually are.)

Brunk, G. G. (2003). Swarming of innovations, fractal patterns, and the historical time series of US patents. Scientometrics, 56(1), 61–80.

Lemley, M. A. (2012). The Myth of the Sole Inventor. Michigan Law Review, 110(5), 709–760. https://doi.org/10.2139/ssrn.1856610

Ogburn, W. F., & Thomas, D. (1922). Are Inventions Inevitable? A Note on Social Evolution. Political Science Quarterly, 37(1), 83–98.