“Who we are and how we got here” by David Reich (a genetics professor who is a big name in the field), is the story of the various migrations and interbreeding of ‘human-like’ and human peoples over the last 50,000 years (with some references going as far back as 300,000 years).
Books on evolutionary psychology might be relevant, simply because evolutionary psychology relies on what evidence we have about how human behaved in pre-history as part of its evidence set. For example, as I recall The Evolution of Human Sexuality had to rely on a lot of anthropological and archaeological research to develop its theory and draw conclusions.
Also, anthropology and archaeology research touch on what it was like to be human before writing. Although ethnographies are a bit out of favor and have some clear issues with observer bias, ethnographies of foragers are probably our best look at what it was like to be a human prior to civilization. Similarly archaeology gives us some insight into what humans were like before writing via the artifacts they left behind, and I think of it as akin to paleontology in that it uses what evidence left to us by the past to infer what it was like: it's not perfect, but it's all we got.
I too was disappointed by the lack of rigor in Yuval Noah Harari's Sapiens. I felt Paleontology A Brief History of Life by Ian Tattersall covered the same material in fewer pages to a higher level of rigor. However, Paleontology might not be the book you're looking for because it covers pre-human natural history too.
I get a lot of quality information from modern ethnographies of hunter-gatherers such as Nisa: The Life and Words of a !Kung Woman by Marjorie Shostak and The World until Yesterday: What Can We Learn from Traditional Societies? by Jared Diamond.
I find the subject of the emergence of language, culture, and society to be quite fascinating. I want to build a more comprehensive model of global prehistory from approximately 200,000 - 3,000 BCE than just "hunter-gatherer societies and spoken language".
I understand that the understanding of these eras is frequently in flux due to the high degree of interpretation required and the scarcity of archaeological evidence, so I am more expecting books that try to give accurate bounds on the events of those areas and not take too many liberties with the available evidence.
Some popular books, such as Yuval Noah Harari's Sapiens, cover the topics I want to learn more about but I think Sapiens is not really the level of rigor for which I'm looking.