Past Subjunctive Sentence

If we started now we would be in time (but we cannot start now)

Like you, I disagree with the book. There is no implication that we cannot start now.

Nevertheless it is the past subjunctive.

If we start now, we will be in time. (present indicative)

If we started now we would be in time. (past subjunctive)

Examples

Mary: Are we ready to start yet?

John: What's the hurry?

Mary: If we start now we will be in time. (indicative)

John: Oh, okay then.

Mary: Are we ready to start yet?

John: What's the hurry?

Mary: If we started now we would be in time. (subjunctive)

John: Oh, okay then.

In neither of the above cases is it impossible for us to start.

If we started now we would be in time (but we cannot start now).

The bracketed bit prevents the usual analysis of the sentence, so I've ignored it for the purposes of this answer.

There's no subjunctive clause in your example. Subjunctive clauses are headed by a plain (infinitive) form of the verb. Some speakers (wrongly) claim that "If I were you" is past subjunctive, but even that doesn't match your example.

"Started" is actually a modal preterite used to mark modality rather than past time. The preterite suggests that we may not start now. There is a choice here between present tense “start” and preterite “started”, which illustrates an important distinction between two kinds of conditional construction, open (with "start) and remote (with "started").

The open type typically leaves it open as to whether the condition is or will be fulfilled.

The remote type, by contrast, presents our leaving as somewhat less likely than the open type. It would generally be preferred where our current plans or inclinations are to leave later.

"If we started now we would be in time"

In the context of being unable to start now, the sentence is the same as "If we could fly, we would be on time." Our ability to start is the same as our ability to fly, i.e. nil. What follows "we would be on time" is fantasy. (Or as it is often described "irrealis" - an unreality.)