Over the course of the museum’s design and construction, Miami-Dade County provided $205 million — some of it as part of a general obligation bond — to enable the project’s completion. Private donations and sponsorships provided most of the rest. Museum officials hope to attract an additional $50 million from naming rights to parts of the facility, which was designed by the British architect Nicholas Grimshaw.

From Mr. Frost’s point of view, the museum was almost too large an enterprise to succeed without pain.

“Through no fault of their own, the people who conceived of it originally were not experienced enough in the area to realize how complex an undertaking it was,” Mr. Frost said. “They might have gone for a less complicated version of the museum, which would have been fine as well. But we have this magnificent institution now and it’s up to the community to support it.”