Sentence:
"Scientists have, so far, only been able to speculate as to why animal species did not (i) $\qquad$ sooner even though offshoots had long started (ii) $\qquad$ once ample oxygen enveloped the Earth's surface."

Context and meaning:
- The sentence suggests that scientists wonder why animal species did not do something sooner.
- Meanwhile, "offshoots had long started" to do something-likely begin developing or increasing.

Thus:
- Blank (i) is something the animal species did not do sooner. It should be related to expanding, growing, increasing, or flourishing.
- Blank (ii) is something the offshoots had started already, likely the same or related action but in progressive/ongoing form.

Analyze options:

For Blank (i):
- A. vanish - to disappear. Does not fit logically with "did not vanish sooner" in this context, since offshoots began something related to growth.
- B. emblematize - to represent symbolically. Unlikely and unrelated.
- C. burgeon - to grow or expand rapidly. Fits the meaning well.

For Blank (ii):
- D. emulsifying - mixing two liquids that normally do not mix. Unlikely in biological evolution context.
- E. vanishing - disappearing. Opposite of what offshoots are doing.
- F. sprouting - beginning to grow or develop. Fits the meaning well.

Conclusion:
- Blank (i): C. burgeon (did not grow or expand sooner)
- Blank (ii): F. sprouting (had long started growing or developing)

Full sentence:

"Scientists have, so far, only been able to speculate as to why animal species did not burgeon sooner even though offshoots had long started sprouting once ample oxygen enveloped the Earth's surface."