The nation's unemployment rate edged up last month to 5.7 percent of the work force, the government reported yesterday, but the number of jobs in the economy continued to surge, indicating the recession is only beginning to take hold.

The July rise, up from 5.6 percent the previous month, marked a full year that the jobless rate has hovered in the 5.7 to 5.9 percent range -- the level most economists now regard as "full employment." The June figure had been a 58-month low.

Yesterday's report showed some weakness in the manufacturing sector: Industry payrolls grew only a slim 44,000 job slots. But total employment, which encompasses a broader measure, soared by 456,000 new jobs -- the second such monthly increase in a row.

The relatively buoyant report appeared on the surface to fly in the face of assertions that the economy is in a recession. A new internal White House forecast predicted this week the jobless rate will leap to 8.2 percent by late 1980.

However, Janet L. Norwood, the commissioner of labor statistics, told a congressional hearing that the jobless rate has climbed that rapidly before, and could do so again. In 1974-75, unemployment soared to 9.1 percent -- from 5.4 percent -- in nine months.

Norwood said the jobless rate typically does not begin to reflect the impact of a recession until well after more sensitive economic indicators. By contrast, output figures -- as measured by the "real" gross national product -- plunged sharply last quarter.

The July rise in the jobless rate was accompanied by an unusually sharp jump in the size of the civilian labor force -- the total of job-holders and job-seekers combined. The labor force swelled by 531,000, outstripping the growth in new jobs.

For all the apparent vibrancy in the nation's job situation, there still were some signs that deterioration may have begun:

The jobless rate for adult men rose to 4.1 percent in July, from 3.9 percent in June -- putting an end of months of relative stability in this key indicator.

The number of jobs in the manufacturing sector continued to decline in July -- a trend that has persisted since last March.

The proportion of unemployed persons who lost their last job, rather than simply could not find a new one, rose to 43.7 percent -- the second jump in a row.

The length of the average work-week for rank-and-file production workers was unchanged in July after failing to rise in June as well.

At the same time, however, apart from the rate for adult men, jobless rates for most other major categories of workers remained unchanged or declined.

The jobless rate for teenagers continued unchanged in July at 15.3 percent. Joblessness among blacks declined to 10.8 percent, from 11.3 percent in June.

Despite the strength in the overall employment figures, analysts cautioned it was too early to draw any firm conclusions from the job statistics.

Norwood told the congressional hearing that the traditional economic indicators were showing "clear signs of difficulty," but said it was hard to gauge the severity of the recession.

And several analysts raised the possibility that the survey on employment may be exaggerating the actual growth in jobs.

The figures were depressed by the April Teamsters' union strike, and have been rebounding since then in part to make up for the interrruption.

The July rise left the actual number of persons out of work at 6.1 million, down from 6.4 million a year ago. CAPTION: Picture, Commissioner of Labor Statistics Janet Norwood discusses the unemployment rate before the Joint Economic Committee. By James K. W. Atherton -- The Washington Post Graph, Unemployment Rate All Civilian Workers, The Washington Post