Yes. The Miami market closes purchases for absent buyers routinely. Property tours run by live video, documents are reviewed and signed electronically where permitted, and the deed and any documents requiring notarization can be executed abroad through a US consulate or, for many countries, an apostilled notarization, or through a power of attorney granted to your representative.
Funds move by wire through the title company's escrow, with the title company verifying the transaction and issuing title insurance exactly as it would with the buyer in the room. Preconstruction purchases are even simpler remotely, since the developer's contract process is built for international execution.
What makes remote buying safe is the quality of the people standing in for your presence. Rangely runs video tours honestly, including the flaws, coordinates the signing logistics with the title company, and handles the whole file in English or Spanish. Many of her international clients first stand inside their property after they own it.