Born in Florence to the patrician Galilei family, he received architectural and engineering training from Antonio Maria Ferri [it], an outstanding figure of the Accademia dei Nobili, who lectured and wrote a treatise on perspective, fortifications and artillery.

Galilei designed the façade of the main block of Castletown, the grandest Palladian house in Ireland, but returned to Italy in 1719 and was not associated with the actual construction of the house, which was begun in 1722 and carried through by the young Anglo-Irish architect Edward Lovett Pearce, who met Galilei in Florence while he was making drawings of Palladio's villas on his tour of Italy.

Once more in Florence after 1719, Galilei was appointed Ingegnere delle fortezze e fabbriche di corte ("Engineer of court buildings and fortresses") of the Grand Dukes of Tuscany, Cosimo III and Gian Gastone de' Medici, last of the Medici grand dukes, neither of whom, however, could provide him with architectural projects suited to his talents.

Galilei's projects during this period included a renovation of the choir of Cortona Cathedral that featured a severely classical triumphal arch motif, additions to the Villa Venuti, at Catrosse, near Cortona, for Domenico Girolamo Venuti, and a design (1724) for the oratory of the Church of the Madonna del Vivaio (since rebuilt) in Scarperia, Tuscany.

The monumental severity and palace character of the façade caused a scandal in Roman artistic circles[4] but was admired later in the century by French and British neoclassicists.