1
In the beginning of the lesson, the teacher checked our homework.
At the beginning of the lesson, the teacher checked our homework.
Use at the beginning of + noun to refer to the first part of a particular period, event or place.
2
At the beginning, the Internet was only a network between a few computers.
In the beginning, the Internet was only a network between a few computers.
In the beginning means ‘at first’ and is often used when the situation changes later.
The purple sentence is possible if the starting point is clear from the context: ‘At the beginning of the Internet’s development…’ However, in the beginning is clearer here.