Summer begins at different times, depending on the definition: Meteorologically always on June 1, calendrically or astronomically at the time of the summer solstice on June 20 or 21, or phenologically with the beginning of the blooming of the peonies and the black elder.
Different beginnings of summer
Every year, when it gets warmer, the question arises when summer actually begins. There are different answers to this question depending on the definition, which will be explained in more detail below.
Meteorological start of summer: Always on June 1
For meteorologists, summer always begins at the same time, namely on June 1, and ends on August 31. It thus lasts exactly three calendar months. The reason for fixing the beginning of summer on June 1 is that for meteorologists, especially in earlier times, whole months were advantageous for easier statistical comparability. The meteorological beginning of summer is therefore completely independent of the weather.
Calendrical or astronomical beginning of summer: June 20 or 21
This is defined according to astronomy: The beginning of summer in the northern hemisphere is when the sun reaches the northernmost point of its orbit and is vertically above the Tropic of Cancer. This is also referred to as the summer solstice.

Fig. 1: Constellation at the astromomic/calendar beginning of summer resp. at the summer solstice; Source: MeteoNews
The day of the astronomical beginning of summer varies between June 20 and 21, because according to the calendar a year lasts 365 days, but the astronomical year lasts 365 days, 5 hours and 49 minutes. To compensate for the difference, there is a leap year every four years. This year, the calendrical beginning of summer is on June 21 at 16:58. The astronomical beginning of summer is thus exactly the same as the meteorological beginning of summer completely independent of the weather.
Phenological beginning of summer: Dependent on weather conditions
Finally, there is also a so-called phenological beginning of summer, which depends on the state of development of nature and which occurs in the lowlands with the blooming of the black elder and the peonies.

Fig. 2: Phenological calendar; Source: MeteoNews
This summer beginning is the only one of the described ones, which is oriented to the weather. According to this calendar, we are recently already in summer, since the black elder and the peonies in the lowlands began to bloom a few days ago.

Fig. 3: Currently blooming peonies in Sarganserland; Source: Roger Perret
Often the phenological spring coincides quite well with the meteorological one and in many cases starts towards the end of May. In a very mild spring like last year, it started as early as mid-May, but in a cool spring like two years ago, it didn't start until early June.
So which is the right beginning of summer?
This question cannot be answered in such a way, since each definition has its right to exist. However, the very variable phenological start of summer best reflects the actual weather pattern and thus certainly best corresponds to human perception. For many, summer begins when it is really warm with temperatures around 25 degrees for a longer period of time. This is usually the case in the second half of May, as it was this year. In the course of climate change, the first summer phase is occurring earlier and earlier on average, in extreme cases even in the first half of May.