"beginning of June" is correct and can be used in written English. It is especially useful for referring to a date within a month. For example, "We are planning to go on vacation at the beginning of June."
They run upriver around the beginning of June.
Those who wish to purchase day passes will get their chance at the beginning of June.
At the beginning of June, the Swiss bank reported a one-year rate of 1.037 percent.
By the beginning of June, the government was ready to act again.
At the beginning of June, "Amnesiac" went on sale in the United States.
If you sow outside, you must wait till the beginning of June.
Warm water is present at MNORTH until the beginning of June. Figure 2: Observations in 2013.
At the beginning of June, both traded at about 10 cents on the dollar.
But the market has had a huge rally since the beginning of June.
The device, which went on sale at the beginning of June, has garnered generally favorable reviews.
Since the beginning of June, investors have pulled $3.2 billion from these funds.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union