Going back sixty years ago would be to 1960. At that point, the "album" as an art form on its own merits was still only at the cusp of being recognized. The 33 1/3 LP had only been available beginning in 1947, and it took several years before it became widely consumed. There were "albums" before 1947 which is where the term "album" comes from. Originally, it was a collection of 78rpm singles of a single artist (or theme) all sold together in a single package. So when the "LP" took the place of the 78 rpm "album" collections, it was viewed the same way—a collection of separate material, not really a cohesive whole. Pop music, and then rock music when it emerged, was still viewed in terms of "singles". The 45 rpm single replaced the 78 rpm single, and well into the LP-era, a "record" still usually referred to these singles. LPs were largely just a repackaging of separate singles by an artist, once the artist had released enough material for an "album". It wasn't until the late 1950s, really, before many artists began recording material specifically for use on an LP. LPs were just collections of their previously-released work.
JAZZ:
The main exceptions to this were classical music and jazz music, who did start to take advantage of the LP format by the late 1940s and early 1950s. Yet, modern music reviews wherein albums are "rated" were still to come. Even in the late 1960s, this style of music criticism was still emerging. One of the early adopters was the jazz magazine Downbeat, which was giving albums ratings in their reviews on a "1-5 stars" scale by the mid-1950s. While I don't have access to their archives, beginning in 1952, they would have a Readers' Poll naming a jazz musician to their "Hall of Fame" each year. Some of these artists' heyday was long before they were named to the "Hall of Fame", though. But in order, Downbeat nominated: Louis Armstrong (1952), Glenn Miller (1953), Stan Kenton (1954), Charlie Parker (1955), Duke Ellington (1956), Benny Goodman (1957), Count Basie (1958), Lester Young (1959), Dizzy Gillespie (1960), Billie Holiday (1961), Miles Davis (1962), Thelonious Monk (1963), Eric Dolphy (1964), John Coltrane (1965), Bud Powell (1966), Billy Strayhorn (1967), Wes Montgomery (1968), Ornette Coleman (1969), and Jimi Hendrix(!) (1970).
They added a Critics' Poll to their "Hall of Fame" beginning in 1961, which added: Coleman Hawkins (1961), Bix Beiderbecke (1962), Jelly Roll Morton (1963), Art Tatum (1964), Earl Hines (1965), Charlie Christian (1966), Bessie Smith (1967), Sidney Bechet (1968), Fats Waller (also 1968), Pee Wee Russell (1969), Jack Teagarden (also 1969), and Johnny Hodges (1970).
The magazine began a Critics' Poll of "Album of the Year" beginning in 1965:
1965: A Love Supreme by John Coltrane
1966: At the Golden Circle, Vol. 1 by the Ornette Coleman Trio
1967: The Popular Duke Ellington by Duke Ellington
1968: The Far East Suite by Duke Ellington
1969: ...And His Mother Called Him Bill by Duke Ellington
1970: Bitches Brew by Miles Davis
ROCK AND POP:
Pop and rock didn't really get anything like the same treatment until the late 1960s. Again, the earliest rock albums were just collections of previously-released singles, and music criticism aimed specifically at these genres didn't really do much in the "rating" department until later. While there were music magazines earlier than the late 1960s, such as Billboard, New Musical Express, and Melody Maker, these were more aimed at sort of the music industry, or music as a product, than at music criticism, or music as an art form.
But in the late 1960s, three rock magazines changed the landscape: Creem (debuting in 1966), Crawdaddy (1966), and Rolling Stone (1967). Each did review albums, though still not with a "star" system until later, and neither did any of them have a "best of" list annually until the 1970s. Creem started a year-end Readers' Poll in 1973, while Rolling Stone didn't have year-end lists until later, and I'm not sure that Crawdaddy ever did.
However, from the original reviews of albums, you can get a sense of what they liked. For instance, in 1966, Crawdaddy reviewed Jefferson Airplane's debut album Jefferson Airplane Takes Off! and the magazine called it "the most important album of American rock issued this year", because it came "out of the new San Francisco music scene (which hopefully means that other groups from the area won't be kept 'underground' much longer)". In a 1967 review, Crawdaddy called the Rolling Stones' Between the Buttons "one of the four or five greatest rock albums ever made".
Probably the first "greatest rock album" really ever recognized was the Beatles' Sgt. Pepper's Lonely Hearts Club Band. Crawdaddy gave it a positive review, actually more than one positive review, running multiple articles over 10 pages of their September/October 1967 edition of the magazine. One of the reviews called it "a monument in rock" and it "is such a dramatic break with the past" that it is worth re-examining all the Beatles' previous work in a new light since it's like "the first album of a new group".
Another of the positive reviews in Crawdaddy ("My Sergeant Pepper Trip"), by Richard Meltzer, was written while the reviewer was high on acid and listening to the album. The book The Crawdaddy! Book: Writings (and Images) from the Magazine of Rock ed. by Paul Williams reprints part of one of these 1967 articles in the magazine, which importantly includes this passage:
"A major indication of the growing importance and prestige of rock is the extent to which the mass media covered Sergeant Pepper—and the way they covered it: not as a phenomenon, but as a work of art to review. Life, Time, Newsweek, The New Yorker, The New York Times all studied the album, and if nothing else at least recognized that the Beatles are true artists rather than a mere pop fad. This may be more-than-obvious, but it's still a major step forward for the mass media, who have always been culture snobs."
In a 1968 edition of Rolling Stone magazine, Langdon Winner wrote in similarly glowing terms of the album:
"The closest Western Civilization has come to unity since the Congress of Vienna in 1815 was the week the Sgt. Pepper album was released. In every city in Europe and America the radio stations played [it] ... and everyone listened ... it was the most amazing thing I've ever heard. For a brief while the irreparable fragmented consciousness of the West was unified, at least in the minds of the young."
One of, if not the only, year-end list to include pop and rock fifty years ago was the one started in 1968 by critic Robert Christgau. That year, he began writing a year-end list of the best in pop for Jazz and Pop magazine. He added a separate jazz list beginning in 1970. When he moved to the Village Voice in 1971, he continued the list as a poll of critics under the name "Pazz and Jop".
For expediency's sake, I'll just include the top three for the three years up to 1970, but each original list includes more than three:
1968:
John Welsey Harding by Bob Dylan
Notorious Byrd Brothers by the Byrds
Cheap Thrills by Big Brother & The Holding Company
1969:
Tommy by the Who
Gilded Palace of Sin by the Flying Burrito Brothers
Beggars Banquet by the Rolling Stones
1970:
Jazz:
Bitches Brew by Miles Davis
Turn It Over by Tony Williams
Devotion by John McLaughlin
Pop:
12 Songs by Randy Newman
After the Gold Rush by Neil Young
Live/Dead by the Grateful Dead
Another source of information is college newspapers. In a May 1, 1969, review of Bob Dylan's Nashville Skyline, a writer for Columbia University's student newspaper the Columbian Spectator called Dylan's previous album Blonde On Blonde from 1966 "probably" "the best album ever".
An article in the December 12, 1969, edition of the student newspaper the Ithacan (Ithaca College, NY) had a semi-"decade's best" list. Actually, the author talks about the "last four years" being transformative, and all the albums he cites come from that period. He names Love's Forever Changes as the "best album" of the period.
Other albums he cites are Jimi Hendrix's Electric Ladyland, Led Zeppelin's I, the "second album" by Country Joe & The Fish (I Feel Like I'm Fixin' To Die), and the Cream album with the "drum solo" (probably referring to "Toad" off of their debut Fresh Cream). He also name-checks a list of other bands and artists of the last four years as putting out exceptional work: the Beatles, Bob Dylan, Traffic, Jefferson Airplane, the Byrds, "and even Larry Hoppen".
TL;DR: There wasn't any consensus, since year-end lists were just starting to emerge 50 years ago, and were non-existent 60 years ago. The album as a unique art form, recognized as something more than just a collection of songs, was just being widely recognized in the late 1960s. Probably the album most widely recognized as the "greatest" before 1970 was the Beatles' Sgt. Pepper's Lonely Hearts Club Band. And among jazz reviewers, Bitches Brew by Miles Davis was recognized as a milestone. Blone On Blonde by Bob Dylan, and Forever Changes by Love were also recognized at least once each as "the best ever". Other work by Bob Dylan, the Beatles, the Rolling Stones, the Who, Jefferson Airplane, and others were being touted as among the best.