"beginning of October" is a correct and usable phrase in written English. You can use it to refer to the start of the month of October, such as in the sentence, "We plan to begin our project at the beginning of October.".
And it's only the beginning of October.
I've been here every day since the beginning of October.
He will receive a sentence at the beginning of October.
One morning at the beginning of October, he was early.
The seeds were harvested manually at full maturity (end of September-beginning of October).
However, at the beginning of October 2010, seismicity increased slightly and the plume activity became somewhat more vigorous (Fig. 3).
The beginning of October 2015 saw headlines nationwide telling of another school shooting in Roseburg, Oregon.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.