At the age of one year, Washington's Metro subway is a surprisingly robust and growing infant, but one that still faces an uncertain maturity.

Its initial downtown line, now five miles long, carried its first passengers on free excursions one year ago today. A total of 51,260 persons rode, jamming many cars so full the system almost broke down.

Two days later - a year ago Tuesday - the clink of coins began in station fare boxes and, since then, some 5,980,000 people have traveled in the sleek cars with the screeching brakes on communting, shopping business and lunchtime journeys.

Lunchtime, in fact, has become a third rush hour for the line, with 30 per cent of riders - some 9,000 - traveling between 11 a.m. and 2 p.m. For Metro planners, the 30,000 daily riders came as a pleasant surprise; they had forecast only 10,000.

Metro's pitch - that it takes just six minutes from Union Station, on the fringe of Capitol Hill, to Dupont Circle - demonstrates how the subway has redrawn the economic geography of downtown, knitting its two ends together with a new dimension of time rather than distance.

Metro will grow by 12 more miles July 1, when a second line opens from Stadium-Armory station through downtown to the National Airport station in Arlington.

More significantly, however, virtually every major office complex in and adjacent to downtown Washington will be served directly by Metro trains when the new line opens: Capitol Hill, Judiciary Square, old downtown, Southwest, Federal Triangle, lower Connecticut, Rosslyn, Pentagon and Crystal City.

Only one significant office complex is not directly served by the trains - the State Department and western Constitution Avenue area.

For all of its potential as a downtown interconnector, Metro still lacks long lines reaching into residential areas. (The first such line, to Silver Spring, is scheduled to open in November.)

For some time Metro will depend heavily upon feeder buses. And future extensions of Metro to fulfill its original 100-mile regional plan are by no means assured.

With costs up sharply - doubled from an original estimate of $2.5 billion at groundbreaking late in 1969 - the construction program has outstripped funds - many contributed by local jurisdictions - available to complete the system.

There was one ray of hope last week. Area jurisdictions completed paperwork on a stopgap financing plan intended to assure completion of a 60-mile network of routes, leaving the other 40 miles up to future political and technical decisions.

The 60-mile system, when completed, would radiate outward from downtown to Rockville-Shady Grove, Silver Spring, New Carrollton, Capitol Heights-Addision Road, Alexandria-Huntington and the Ballston station at Glebe Road in Arlington.

Other extensions remain uncertain, largely because the federal government has told regional officials to study less costly alternatives to the rail network.That study will be completed in the summer, to be followed by drafting of a new financial plan.

Left in limbo by the study is Washington's midcity line, with extensions that would poke deeply into Prince George's County.

Meanwhile, trains will continue to run on the existing line 6 a.m. and 8 p.m. weekdays, with longer hours - and perhaps seven-day-a-week service - deferred at least until 1978.

Although the daily passenger volume is much greater than expected, the line falls far short of breaking even financially. Fare collections have totaled only $2.6 million in the past year (many passengers have used transfers to board the trains), while costs have reached $17.2 million, much for training and testing.

Initial fears of crime have proved wrong, partly because of an active Metro Transit Police force. There have been only 27 arrests, mostly for disorderly conduct.