Не успела я поехать, как перед машиной появился пешеход, и я сразу нажала на тормоз.

I barely started driving when a pedestrian appeared in front of the car, and I immediately hit the brake.

Breakdown of Не успела я поехать, как перед машиной появился пешеход, и я сразу нажала на тормоз.

• я: I
• машина: the car
• перед: in front of
• и: and

Questions & Answers about Не успела я поехать, как перед машиной появился пешеход, и я сразу нажала на тормоз.

Why does the sentence start with Не успела я поехать? What does this structure mean grammatically?

Не успела я + infinitive, followed by как ..., is a common Russian pattern meaning “No sooner had I … than …” / “I barely managed to … when …”.
Grammatically, не успела is past tense (feminine singular) of успеть (to manage / to have time), and поехать is an infinitive that completes the meaning: “I didn’t have time to set off (before…)”.

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Why is it не успела (feminine) and not не успел?

Past tense in Russian agrees with the subject in gender and number. Since the subject is я and the speaker is presented as female in the sentence, it becomes не успела and later нажала.
If the speaker were male, you’d get не успел я поехать … и я сразу нажал ….

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Is я required here? Could it be omitted?

It’s optional. Russian often drops personal pronouns because the verb ending already shows the person (and in past tense also gender/number).
Both work:

• Не успела поехать, как… (more neutral/flowing)
• Не успела я поехать, как… (adds emphasis/contrast: me specifically)

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