In English, both "at the beginning of September" and "in the beginning of September" are sometimes used interchangeably to mean the same thing — the early part of September.
However, "at the beginning of" is considered more standard and more commonly used. It indicates a more precise point in time, typically the first few days of the month, week, etc.
For example:
1. "School will start at the beginning of September." — This would generally be understood to mean school starts during the first few days of September.
The phrase "in the beginning of" is often less preferred in this context, and some style guides may even consider it incorrect. However, it's still understood by most English speakers. If used, it typically carries the same meaning as "at the beginning of," indicating the early part of the time period.
For example:
2. "School will start in the beginning of September." — This sentence, while less standard, is still understood to mean school starts during the first part of September.
When in doubt, use "at the beginning of" for clarity and conformity to standard English.