What is "一" doing in "事情一开始进展得很顺利，但后来我们遇到了困难"? 事情一开始进展得很顺利，但后来我们遇到了困难


I understand the meaning of the sentence, but I don't understand what is "一" doing in there? Could it be dropped? Would it change the meaning? Is it a part of the "一开始" as a phrase?
一 in this construction has the meaning of ”once”.

Once the business got started it was very successful, but later on we encountered difficulties.

Another example: 一看他的样子就知道他是个骗子。