Kwame Nkurumah and Julius Nyerere were the leaders of Anglophone Africa's pan-Africanist movement. As a result they were keen on appropriating/transforming what they deemed to be inherited colonial political formations in a way that would resonate with what they imagined to be more "authentic" African political structures. This laid the intellectual groundwork for a more inclusive electoral system that appealed to "African" and national identities over the exclusivist ethno-politics that came to characterize even relatively stable African democracies like Kenya.

Though Ghanian democracy (and Tanzanian democracy for that matter) was wobbly at first and the 1966 "Cold Chop" coup deposed Nkurumah, political transition in Ghana never involved a "purge" cycle that produced "zero sum" stakes of electoral politics.

So, despite a long series of military dictators, the multiparty reforms and elections of 1992 produced an elected official, and since 1992 Ghana's prime ministers have all been the products of elections. This includes 3 peaceful transfers of power. This is a remarkable record in the African electoral landscape.

To answer your question, we could probably point to 1992 as the date that multiparty democracy was born in modern Ghana, but I think the ideological foundations of Ghanaian inclusive politics owe much to Nkurumah's legacy.