height of, thick of, full swing
酣 centers on the peak or most intense point of an activity or state: the height of something, the thick of an event, or being in full swing.
酣 combines 酉 (sake jar) with 甘 (sweet), suggesting the peak of intoxication or enjoyment. The exact historical development is uncertain, but the component combination likely points to the height of a drinking experience.
The sake jar 酉 and sweet 甘 together suggest the sweetest, most intense moment of drinking—the height of the party, when things are in full swing.
For カン, imagine a can of sweet sake being opened at the peak of the celebration: can -> カン, and the party is in full swing.