I achieved this on Day 55 without real issue. The first mission goal reward when playing as China, for producing 100 food, is an additional 100 applicants. That, plus the initial pool of 200 should allow you to fill your colony to 200 even when restricting specialisations for passenger rockets to the fields you need.
I took the Inventor profile for Autonomous Hubs to speed expansion.
I built out as follows:
4 micro domes (2xMetal Extraction, 1xMachine Parts, 1xNursary/School)
2 basic domes (1xfarm, 1xhousing with polymer factory outside)