Maddie and Tom never stopped looking for any of their sons. The real reason Tom became a Police was to try finding anything on them. They were about to give up when Sonic found them. They all took a DNA (with consent) test and were waiting for the results when it finally came. It came back positive, and maddie and tom were over joy and happy. Their hope was renewed.
When Sonic found the picture of three boys. He asked Maddie and Tom, who they were. When Maddie and Tom realize they forget to tell Sonic their his biological parents. That was when Sonic found out about his big brother and little brother.
He was overjoyed and asked if they were looking for them. Tom nodded and said yeah they were. Sonic asked what their names were. After that, Sonic asked almost every day if they found anything.
(Also, Robotnik is a rival school principal who is trying to win the emerald reward for best school)