Based on discussion by Latin grammarians such as Diomedes and Priscian, plus interchange between "PH" and "F" in spelling (nicely summarized by the graph in Alex B.'s answer) it seems clear [f] was a usual pronunciation of PH in Latin by the 5th century AD. (I'm confident in this as a terminus ante quem.)
Dating when this pronunciation began to be used is a bit tricky. There are several possible inscriptional examples of F used for Greek Φ before the 1st century AD. (It seems however that the identification of the letter or of the name is sometimes arguable.)
CIL I² 2652: The reading HELIOFO seems to be generally accepted, although an alternative reading HELIODO(RUS) has apparently been considered. Biville dates this inscription to before 88 BC. The inscription appears on a altar in a shrine next to the entrance of House 1D in the Stadion/Stadium district of Delos. In support of the reading HELIOFO, the name ΗΛΙΟΦΩΝ appears written in Greek script inside of House 1D. I haven’t found a photo of this inscription yet. Zarmakoupi 2016:65 cites Plassart 1916:211 as a source.
CIL I² 753 has been read as showing the name "ORFEUS" but it has been argued that "ORPEUS" is actually the correct reading (Buchholz 2014:260). Biville dates this inscription to 59 BC (citing Biville 1990:191).
CIL I² 1413 has been read as showing the name "FEDRA" (Buchholz 2014:260), but it has been argued that "FLORA" is actually the correct reading (Adams 2007:82, citing ILLRP 809). Purnelle 1995:228 dates the inscription to the first century BC and likewise notes the doubt about whether it reads "FEDRA" or "FLORA".
(These bullets were written in response to a deleted answer by a now-deleted user that cited Frédérique Biville's Les emprunts du latin au grec: Introduction et consonantisme, 1990:191, which mentions these three inscriptions as examples of Republican Latin use of F for Φ.)
However, there are reasons to suppose that in the first century AD, the identification of the sounds of "PH" and "F" by Latin speakers was not complete (regardless of whether it had begun). Quintilian, writing in about 95 AD, implies in the following passages that the sound of Latin ⟨F⟩ did not occur in Greek:
"nam contra Graeci adspirare ei solent, ut pro Fundanio Cicero testem qui primam eius litteram dicere non possit inridet." (Institutio Oratoria 1.4.14)
"Et velut in locum earum succedunt tristes et horridae, quibus Graecia caret. Nam et illa quae est sexta nostrarum, paene non humana voce vel omnino non voce potius inter discrimina dentium effiandaest; quae, etiam cum vocalem proxima accipit quassa quodam modo, utique quotiens aliquam consonantem frangit, ut in hoc ipso frangit, multo fit horridior." (Institutio Oratoria 12.10.28)
(The exact interpretation of these passages has been subject to a certain amount of debate; in particular, before the second passage, Quintilian gives two Greek words as illustrations of two pleasant Greek sounds that Latin lacks, and it is debated what the words and what the Greek sounds in question were.)
It is clear that Greek speakers systematically used Φ to represent Latin "F", starting from an earlier point than the frequent use of F in Latin to represent Greek Φ. The consensus is that this convention initially was a case of Greek speakers using an aspirated bilabial plosive [pʰ] as the closest sound in their native inventory to a labial fricative [f]. There are examples of similar adaptations in modern languages, such as Korean 커프스 [kʰʌpʰɯsʰɯ] from English cuffs. (Of course, after Greek Φ had attained its current pronunciation as a labial fricative, the equivalence to Latin F is trivial.)
The use of Φ in Greek of all periods as the regular representation of Latin "F" raises the possibility that early cases of inscriptional "F" for Φ might represent the pronunciation of a native Greek speaker with Latin as a second language, rather than indicating a correspondence between the sounds of "PH" and "F" in the mouths of native Latin speakers. I am not sure however if this explanation is plausible for any of the specific inscriptions cited above.
References
Adams, J.N. 2007. The Regional Diversification of Latin 200 BC - AD 600. Cambridge University Press.
Biville, Frédérique. "La graphie des noms propres en contexte multilingue" in : Ruiz Darasse, Coline, Comment s’écrit l’autre ? Sources épigraphiques et papyrologues dans le monde méditerranéen antiques, Pessac, Ausonius éditions, collection PrimaLun@ 1, 2020, 15-28 [online]
Buchholz, Laura. 2014. "Re-edition of AE 1922, 126: The Earliest praefectus lege Petronia?" Zeitschrift für Papyrologie und Epigraphik, 190, pages 257–261
Plassart, André [citation as given by Zarmakoupi; not personally consulted by me] 1916. “Fouilles de Délos, Exécutées aux Frais de M. Le Duc De Loubat (1912–1913): Quartier des Habitations Privées à l’Est du Stade (pl. V–VII).” Bulletin de Correspondance Hellénique 40: 145–256.
Purnelle, G. 1995. Les usages des graveurs dans la notation d'upsilon et des phonèmes aspirés: le cas des anthroponymes grecs dans les inscriptions latines de Rome.
Zarmakoupi, Mantha. 2016. "The Spatial Environment of Inscriptions and Graffiti in Domestic Spaces: The Case of Delos", Chapter 4 in Inscriptions in the Private Sphere in the Greco-Roman World, Rebecca Benefiel and Peter Keegan (editors), Brill.