Most Florida probate courts simply accept the information contained in the pleadings that are filed with the court. These pleadings are usually signed “under penalties of perjury”.
Some courts (such as Citrus Count and Miami-Dade County) often require an Affidavit of Heirs.pdf to be filed along with the pleadings. There really is no other independent evidence that is required to prove who the beneficiaries are.
When a rightful heir has been omitted from the pleadings, it is important to act timely. Sometimes, there are people who are included that should not receive a portion of the estate.
If anyone (most likely one of the heirs) contests the proposed distribution of assets by claiming that one or more of the alleged heirs are not heirs at all, there will be an evidentiary hearing where the disputed heirs will need to prove they are heirs. (A Birth certificate is a good start on this).
Generally, the Affidavit of heirs contains information on the spouse, children of the decedent, the surviving spouse, children of the surviving spouse, parents, siblings, grandparents, aunts, and uncles.