I am aware of the fact that Communist movements and organizations, such as the League of the Just in 1836, existed prior to Marx, but I haven't been able to find much of a concrete explanation on the ideological underpinnings and organizational structure of these movements and organizations that existed prior to Marx and Engels publishing the Communist Manifesto other than the fact that they tended to be more based in Christianity, and Marxist Communism was more atheistic or at least secular (and I know that the "opiate of the masses" line is often cited sans context). But other than that, I don't know much. Would they have called themselves "Communists" or was that a Marx invention. Was their perspective on the nature of the relationship between the Bourgeois and the Proletariat similar to Marx's or different or was the class struggle concept absent (or much less prominent) altogether? What was their relationship to socialism, or was the distinction seen at all, prior to Marx's vision of it as a stage following capitalism, but preceding communism?
"Pre-Marxist communism" is a label that serves no function. Marx coined the term "communism" and preceding theories of social and economic organisation that may resemble communism should not be referred to as such. They can be described as egalitarian, classless states but labelling them as "communist" is inaccurate.
Furthermore you seem to be suggesting that the Communist Manifesto was the beginning of communism, this is also somewhat inaccurate. By in large, the 'Communist Manifesto' is not as developed in terms of Marxist economic and philosophical thought as other works. Many regard the 'Economic and Philosophic Manuscripts' published in 1844, four years prior to the manifesto, to be far more informative in that sense. Marx also published a few more works that detail his Hegelianism in the early 1840s before the Manifesto's release so communism most certainly did not begin with the 'Communist Manifesto'. 'Das Kapital' is the obvious juggernaut of classical Marxism but with regards to your question, it was published much later.
If you are looking for a history of societies and theories that resemble Communism I can highly recommend 'Communism: A History' by Richard Pipes (1994) or 'The Red Flag: A History of Communism' by David Priestland (2009). I believe some examples of pre-Marx societies/theories with egalitarian and classless-society values are discussed in these two books.
Apologies for potentially awful formatting.