I agree with Barnes’ commentary on 2 Cor 6:2 that a “favorable time” refers to the time of the Messiah. It is favorable because it is a time marked by God’s favor, His mercy and grace, upon men. In my opinion, the time that is ushered in by Christ is also favorable because, within the course of human history and development, it is a time deemed favorable by God for the bestowing of the gospel and the salvation of men.
For he saith - see Isaiah 49:8. In that passage the declaration refers
to the Messiah, and the design is there to show that God would be
favorable to him; that he would hear him when he prayed, and would
make him the medium of establishing a covenant with his own people,
and of spreading the true religion around the earth…
Under the Messiah, it is said by Isaiah, God would be willing to show
mercy. That would be an acceptable time. That time says Paul, has
arrived. The Messiah has come, and now God is willing to pardon and
save. And the doctrine in this verse is, that under the Messiah, or in
the time of Christ, God is willing to show mercy to people. In him
alone is the throne of grace accessible, and now that he has come, God
is willing to pardon, and people should avail themselves of the offers
of mercy. – Barnes commentary, biblehub.com
“With God, ‘with whom there is no variation’ [James 1:17], how can one time be any different from another?” Regarding the OP’s last question, I can only offer my personal point of view. The nature of the world and of human life is flux and change, and the notion of time itself is inextricably linked to that reality (“What is Time?” sciencealert.com). While God, who is the Creator of it all, is not bound by time, He may appear so to us whose existence is in many ways defined by our experience of time.
That said, if we look at the verbs in 2 Cor 6:2, both the present and aorist tenses present a complex picture of how God acts and works within human history to fulfill his unchanging purposes and plans, plans that can be considered as already completed (cf Is 14:24).
For he says (present), 'In a favorable time I listened (aorist) to
you, and in a day of salvation I have helped (aorist) you.'
The present tense of “says” reflects the unchanging nature of God’s words such that what he says in Isaiah, he says to each successive generation (cf Is 40:8). The aorist tense on the other hand gives us a sense of God’s perspective from a vantage point outside of time. According to Bill Mounce, the aorist is much more than past time:
“I like Con Campbell’s word picture of the aorist. You are in a
helicopter over the parade, looking at the parade as a whole. Buist
Fanning talks about seeing the action from the outside as a whole
rather than from inside the action – “The Aorist is so much more than a
past tense,” billmounce.com
Because God sees the whole arc of human history from beginning to end (cf Is 46:10), both that of humanity in general and of each person in particular, He alone can choose a favorable time to suit His purposes and our needs. In that favorable time, what God has spoken He will unveil and what God has promised He will fulfill.
But their minds were made dull, for to this day the same veil remains
when the old covenant is read. It has not been removed, because only
in Christ is it taken away. 15 Even to this day when Moses is read, a
veil covers their hearts. 16 But whenever anyone turns to the Lord, the
veil is taken away. – 2 Cor 3:14-15