Can I hire one full-stack developer to build the whole thing?

Possible but risky. A senior generalist can ship a small MLM platform in 4 to 6 months, but bus factor is brutal: if the developer leaves or becomes unavailable, the platform stops. Better to pair the senior generalist with a junior or a QA contractor for redundancy. For engagements over $30K, single-developer-no-redundancy is the structure that produces the most catastrophic failure modes when something goes wrong with the relationship. Either insist on a small team or shift to an agency engagement where redundancy is structural.