Reincarnation of the consciousness is inevitable

[Jackalope]

How am I "affirming the consequent"?

To demonstrate, I'll have to untangle the first part of the argument.

P1) If time was not infinite, there could be no point in "time" for which time could start.
C1) Therefore time is infinite.

I'm taking a stab at what I think your argument is, let me know if this doesn't capture it (I had to remove the "not" from the P1 and add P2 which seemed to be implied by the argument):

P1) If time was infinite, there could be no point in "time" for which time could start.
P2) There is no point in "time" for which time could start.
C1) Therefore time is infinite.

The syllogism is then of the form:

P1) If P then Q
P2) Q
P3) Therefore, P

This is not a valid syllogism (and in fact is a textbook example of affirming the consequent). A valid syllogism would be of the form:

P1) If P then Q
P2) P
P3) Therefore, Q