It wouldn't really be called a date by a passerby's eyes. It would look like a jovial family outing, with a Human child balanced on a tall skeleton Monster's shoulders, and a skeleton Monster smiling easily as he walked hand in hand with a laughing goat Monster.
It was a good date, with familial love and the beginnings of romantic love between Toriel and Sans.
To love each other was to love each other's family members.