I'm new to Sai Baba and have some doubts. Was it common for people to be skeptical when they first met him, and how did Baba handle their doubts?

Yes, it was not uncommon for visitors to approach Sai Baba with skepticism. The story of Boss Dharamsee in Chapter 35 provides a clear example. He arrived with a 'clinical scrutiny,' intending to observe Baba with a critical eye. When Baba offered him grapes with seeds, a variety he disliked, Dharamsee's doubt intensified, and he questioned in his mind if Baba was a true saint. Instead of addressing this verbally, Baba gave him even more grapes and commanded him to eat them. The miracle that followed—the grapes becoming seedless—directly addressed Dharamsee's inner state, causing his ego to drop and transforming his doubt into faith, as Chapter 35 beautifully illustrates.