kiss (someone's) baby

Translations
разыгрывать симпатию (у избирателей)
During the campaign, the politician was seen kissing babies at the local fair.
Во время кампании политика видели, как он разыгрывал симпатию у избирателей на местной ярмарке.
Definitions
To kiss someone's baby refers to the act of a politician or public figure kissing a baby in public, often as a gesture to appear friendly, caring, and relatable to voters. It is commonly associated with campaigning and efforts to gain public approval.