This is one of those questions that's going to be tough to answer with an authoritative source, because "how easy it was to get a job 50 years ago," is not a frequent topic for historical analysis.

Obviously, anecdotal sources abound, but anecdotes aren't hard evidence. So let's start with what we do know, economic data. That can give as an answer in a backwards way.

from 1960 to 1973 the average unemployment in the United States was 4.9%

This article suggests that unemployment declined as a result of Johnson administation policies to a low of 3.6% by 1968 (but at the same time the inflation rate was 6% per year).

Among adult male full time workers the unemployment rate was 3.2% and the mean time of unemployment was 13 weeks. Source

That's getting awfully close to what modern economists would view as "full employment." That is the concept that just about everyone who wants a job is able to obtain one. Those that remain unemployed are those sick, in school or not seeking work for some reason.

The minimum wage in 1960 was $1.00 per hour. But with adjustments for inflation that works out to be somewhere between $9.22 and $10.52 per hour today.

This also summarizes some of the job programs that were created in the 1960's

This brookings institution article recites that there were recessions in 1958 and 1961, but:

Finally, as unemployment fell in the1960s, reports of labor shortages were heard with increasing frequency, and dissident movements in unions led to contract rejections and pressures on incumbent union officials.2 Concession bargaining waned.3

It cites as data that by 1966, virtually no union negotiated contracts included wage concessions (rather the Union contracts substantially included wage increases on re-negotiation).

That same source also recites that in 1970 (at the tail end of this period) youth participation in the labor force was 21% compared to 18% in later years (and lower today).

The Brookings source also contains this passage:

However, the real flood of labor shortage articles began in late 1965, articles whose flavor can easily be sensed from their titles: "Help Wanted-Almost Everywhere," "Too Much Employment?," "Skilled Labor Pinch Gets Tighter," "Labor Shortages Become Acute," "Help Wanted-And Very Badly." Other articles suggested solutions for employers such as obtaining foreign labor, stepping up internal training programs, or enlarging job duties of existing workers.

This new york times article from 1973 takes a different tack and recites that 2/3rds of job growth in the 1960's went to women and minorities, but keep in mind thsi is against a blackdrop of the 1950's when "pink jobs" were far more common (i.e. women were limited to traditionally female occupations), white men would have had much closer to full employment to begin with.

So what does all of this economic data tell us?

it's likely that the anecdotes about the ease of finding work have a measure of truth to them. Particularly in the mid 1960's, 64-68 or so, the country was at extremely low unemployment during that time period, and media during the time period were discussing a labor shortage. Large numbers of women and minorities who had previously been excluded from the job market were finding jobs. unions were far more aggressive in negotiating new contracts (which creates an inference that the Unions were not concerned about the possibility of the employers cutting jobs).

This suggests that a white male 18 year old seeking a semi-skilled manual labor job during that time period likely would not have a lot of difficulty finding such a job, and in a time of expanding union participation and aggressive negotiations, union jobs would have been more common than they are today.