The Fictional Date
If Quantez happened in the real world in a real period of history, it would be easy to narrow down the date, perhaps even narrow down the date so much that no time in real history would fit.
The minstrel character sings a ballad about the famous gunslinger John Coventry mentioning old Tombstone. The boom town of Tombstone, Arizona was officially founded on March 5, 1879, and flourished until the pumps that kept water out of the mines burned on May 26, 1886, and the price of silver plummeted soon after, turning Tombstone into almost a ghost town. The ballad gives the impression that John Coventry was active when Tombstone flourished in 1879-1886 and that Quantez happens after 1886.
Delgadito (Michael Ansara) has the same name as a real chief of the Mimbreno Apaches. But Delgadito flourished before the the US Civil War in 1861-1865, and was probably dead for years when his superior in the movie, Victorio, became famous.
Gato, a white man who thinks of himself as an Apache, left Cochese's peoppel after Cochise made peace. In Broken Arrow (1950) Cochise made peace in 1870, and in Taza Son of Cochise (1954) in 1872; the historic date was October 12, 1872.
In Quantez, Delgadito says that Victoria is preparing for all out war with the whites. Victorio (c. 1825-1880) had an up and down relationship with the USA for many years. From 1870 to 1880 his Mimbreno Apaches were moved to and left three different reservations. In late August 1879 Victoria and his followers left the reservation and began Victorio's War which terrorized white southwesterners for over a year.
On October 14, 1880 Mexican soldiers surprised and killed Victorio and many of his followers at Tres Castillos.
So there would be a period of about 1 year, 7 months, and 9 days for John Coventry to make a name as a gunslinger in Tombstone after it was founded on March 5, 1879, and before Victorio was killed on October 14, 1880. Of course it could have taken Delgadito days or weeks to hear about Victorio's death, and maybe Delgadito keep it secret from his men for a while to keep them from giving up, so the period could be a little longer.
But Delgadito says that Victorio is preparing for all out war, indicating the date is before late August 1879, and thus less than 6 months after Tombstone was founded. That John Coventry must have done something really spectacular in Tombstone for the minstrel to already be singing about it.
How does Quantez fit in with other movies and TV shows featuring Victorio?
In Hondo (1953) Apache chief Vittorio is killed at a fictional date of probably 1870. Vittorio is more or less a variant of the name Victorio, so it is commonly assumed that the character Vittorio is based on the historic Victorio.
In Apache Rifles (1964) Victorio, Chief of the Mescalero Apaches, is killed in Arizona Territory in 1879, and his son Red Hawk becomes chief of the Mescaleros who are transferred to a reservation in Texas.
Apache Drums (1951) opens with the statement that Victorio, Chief of the Mescalero Apaches, declared war on the white men in New Mexico in 1880 and includes Victorio's death there. Is he the same Victorio brought back to life or another Apache chief with the same name?
Victorio is killed attacking Fort Bowie in Fort Bowie (1958) at a fictional date that is probably in or after 1881. Is he the same Victorio brought back to life or another Apache chief with the same name?
In Tomahawk Trail (1957) Victorio survives the movie, but no date is given.
So if Quantez happens in the same fictional universe as other western movies it's Apache leader Victorio could have been active at about any date from 1865 to 1900 as far as consistency with other movies is concerned.