Before the death of Lazarus, Jesus had already raised others from the dead:  "Jesus went to a town called Nain…….where a dead person was being carried out……..He said, 'Young man, I say to you, get up!'  The dead man sat up and began to talk, and Jesus gave him back to his mother."  Luke 7:11-15  NIV    Also:  "A president of the synagogue, called Jairus, came up……'My little girl is dying; do come and lay your hands on her, that she might recover and live'…..A message came from his house, 'Your daughter is dead.'  Jesus went to his house, took the girl's hand, and said, 'Little girl, rise'.  The girl got up at once and began to walk."  Mark 5:22-24, 38-42  Moffatt

In each of these cases Jesus brought the person back to life very soon after death, leaving his detractors the opportunity to doubt if they had ever really been dead.  When Lazarus died, Jesus deliberately waited until he had been dead four days, until even Mary protested that putrefaction had set in.  He explained his delay to his disciples, "I am glad for your sakes that I was not there, to the intent that ye might believe."  John 11:15

In commanding that Lazarus come forth, Jesus prayed aloud to His Father, in front of numerous witnesses, "'I know You always hear and listen to me; but I have said this on account of and for the benefit of the people standing around, so that they may believe You did send me–that You have made Me your Messenger.'…..Upon seeing what Jesus had done, many of the Jews who had come with Mary believed on Him–they trusted in Him and adhered to Him and relied on Him."  John 11:42, 45  Amplified