Learn Farsi: این یک تغییر بزرگ است.

That hidden sound is the ezafe. It is an "e" sound connecting the noun تغییر (change) to its adjective بزرگ (big), making it pronounced as "taghyir-e bozorg". It is almost never written in the Persian alphabet, but you must say it to link the words together.

In English we say "big change", but here the words seem flipped. Why?

In Farsi, nouns almost always come before the adjectives that describe them. So "a big change" translates to یک تغییر بزرگ (literally: a change big).

Why does یک (a/one) come before the noun, when the adjective comes after it?

While descriptive adjectives follow the noun and use an ezafe, numbers and quantifiers like یک (one/a) come before the noun. Notice that you also do not use an ezafe between یک and the noun it counts.

Why is است (is) placed at the very end of the sentence?

Farsi sentence structure is Subject-Object-Verb. This means the main verb is almost always placed at the very end of the sentence. Here, the subject is این (this) and the verb است (is) waits for the end.

How would I change this sentence to say "This might be a big change" using the grammar from this lesson?

You would add the impersonal modal شاید (might) and change the indicative verb است (is) to its present subjunctive form, (be). The new sentence would be: .