初め and 最初: an opening period and the first item
Compare the beginning of a month with the first arriving customer, and distinguish reading the first page from a first-ever experience.
The opening part of a period or process
初め, read はじめ, can identify the beginning of a period or process. 月の初めは忙しいです。 says that the beginning of the month is busy.
初めのうちは道に迷いました。 says that the person got lost during the initial period. It need not restrict that period to the first day alone.
The first item in an order
最初, read さいしょ, identifies the first among several items. 最初の客は九時に来ました。 says that the first customer arrived at nine.
最初に名前を書いてください。 asks for the name to be written first. It specifies an order relative to the steps that follow.
Overlapping uses and different information
Both 初めに説明を聞きました。 and 最初に説明を聞きました。 can say that the explanation was heard first. The words are not always mutually exclusive.
最初のページを読みました。 says that the first page was read. This differs from 初めて読んだ, which identifies a first experience of reading.
Does 最初のページを読みました。 establish a first-ever reading of the book?
Show the answer and why
No. It specifies the page’s position. Whether the book had been read before needs separate information.