People ascribed many different titles to Jesus in his lifetime with “Son of God” being chief among them. He never protested or corrected people when they called him this (see Matthew 14:33 and 26:63).
On the other hand, although Jesus didn’t openly walk around Palestine with a megaphone claiming, “I am God — come follow me!” there were times, especially in John’s gospel, when he talked in theological terms that some people would have recognized as equating himself with God.
For example, in the Hebrew Scriptures, God revealed his name to Moses in the riddle-like form of “I AM” (then translated to Yahweh). I AM — or Yahweh — was the primary name for the Divinity. In John’s gospel, Jesus revealed himself as “I AM” on several occasions, the first being to the Samaritan woman at the well in John 4:26 (not to one of the men in his inner circle of friends, but to her!). Once, when he declared himself as I AM, his opponents were so offended and infuriated by it they attempted to stone him (John 8:58-59). Most of the time, though, Jesus humbly let others recognize him by his works and let their declarations serve as his advertisement, as when doubting Thomas saw Jesus’ scars and burst out, “My Lord and my God” (John 20:28).