In Mark, "the time" being reference is a period of time.
From Marvin R. Vincent's study of Mark 1:
The time (ὁ καιρὸς)
That is, the period completed by the setting up of Messiah's kingdom.
Compare the fulness of the time, Galatians 4:4.
Also, if you compare your translation to other translations you can see that "at hand" is also often translated as "is near", meaning it has not yet arrived, but is coming soon.
Paul seems to define the Good News as "What God promised our ancestors he has fulfilled for us, their children, by raising up Jesus." In Mark, Jesus could be referring to his resurrection and rising to Heaven which will be happening in the near future, and not necessarily his birth and initial time on Earth.
I like Acts 13:32-35 for a definition of the Good News by Paul. Here he is actually referencing Psalms and Isaiah.
Acts 13:32-35 (NIV) (Paul speaking)
32 "We tell you the good news: What God promised our ancestors 33 he has fulfilled for us, their children, by raising up Jesus. As it is written in the second Psalm:
"'You are my son;
today I have become your father.'
34 God raised him from the dead so that he will never be subject to decay. As God has said,
"'I will give you the holy and sure blessings promised to David.'
35 So it is also stated elsewhere:
"'You will not let your holy one see decay.'
Acts 13:38-39 tells how through Jesus we are forgiven and freed from sin.
Acts 13:38-39 (NIV)
38 “Therefore, my friends, I want you to know that through Jesus the forgiveness of sins is proclaimed to you. 39 Through him everyone who believes is set free from every sin, a justification you were not able to obtain under the law of Moses.