There may be significance in noting the purpose of the signs Jesus performed, starting with the first one that marked the beginning of his ministry. This took place at the wedding in Cana, where Jesus turned water into the best of wine.
John's account notes this as the beginning of the signs that Jesus did. But perhaps the important part of the sentence is the latter half which adds that (by this) he manifested his glory, "and his disciples believed in him".
Note the progression - Jesus' signs manifested his glory, causing others to believe, and to believe in him.
Note the difference when others saw his miraculous signs, or asked him to perform some sign, but for the wrong reasons. They wanted miraculous signs, but they did not 'want' Jesus. They claimed that they would believe if they got what they asked for, yet Jesus refused, saying their desire was that of a wicked and adulterous generation (Matthew 12:39). They wanted signs for the sake of signs - not what those signs were pointing to - the promised Messiah in their midst. They were unbelievers in the glory of Jesus, and even if he obliged and performed a miracle just to impress them (which he would never do) that would not have the same result as in John 2:11, where the disciples saw the glory of Jesus through that sign, and believed in him.
A sign points to something. It is not the sign that matters - it is only if the person sees what the sign points to that the sign serves its purpose. This is shown with the beginning of the signs Jesus performed, through every last one of them. The glory of the Lord was evident in those signs, so that all who saw that saw Jesus, and put their faith in him.
The answer to your question, then, is that John 2:11 speaks of the beginning of the signs Jesus did. It is as simple as that, and the verse itself simply states that.