No. The protocol defines the supply, issuance and inflation rate, but - assuming we are talking about a decentralized network - a single actor cannot manipulate it. Solana is an example of a centralized crypto currency upheld by a single entity.
> whoever got hold of the initial supply will be richer (in Solana) than anyone who didn't get there in time
The same happens with US dollars. It has a limited supply, but more is printed and entered into circulation each year, creating inflation. This is like a decentralized crypto currency, but in US dollars a single country controls the circulation, and users of the currency cannot fork the protocol.
Bitcoin is one of the few popular crypto currencies that aims to have a hard limit in total supply with no plans for adaptive issuance or inflation.