The traditional pattern of American war making from the War of Independence through to World War II was to raise troops for the occasion and to otherwise rely on a small, poorly funded professional nucleus around which a larger volunteer (later, draftee) army could be built. This is tied up with a long-standing fear of standing armies and abhorrence of the expense involved in keeping one up.

If one looks at the American Civil War, for instance, the professional army on the eve of war was 16,000 officers and men; the navy consisted of about forty ships in commission, many of them antiquated. The army in particular was heavily dispersed, being composed of detachments spread between coastal forts and frontier posts. This tiny force would be massively supplemented by 2.2 million volunteers and conscripts during the war. The navy would swell to include more than 700 ships and ironclad monitors.

With peace, a massive reduction in force took place. The navy shrunk to a size barely larger than before the war. It would be built up again starting in the 1880s and 1890s, becoming the fifth largest in the world by c. 1900. But the regular army would remain very small indeed; in 1898, it numbered some 28,100 officers and men. In order to prosecute the Spanish-American War, volunteers were called for, and more than 220,000 answered.

The army would grow substantially over the next decade and a half, reaching some 98,000 men in service in 1914, 45,000 of whom were stationed overseas. An additional 27,000 men were in the National Guard. This was still a paltry force by European standards, and though it was increased by some 40,000 before American involvement in WWI began, it was necessary to draft 4,000,000 men to prosecute the war.

After the war, the army desired a permanent expansion to approximately 500,00 men, as well as a national training program to enable ready expansion, but this they did not get. The National Defense Act of 1920 established a theoretical army of 300,000, but this would be repeatedly cut in the 1920s until reaching a strength of approximately 137,000, which it would remain until 1936. Budgets were extremely tight, and modernization of equipment was basically impossible. Tanks and aircraft in particular were antiquated in the extreme. The navy remained the only viable element of the US military during this period, though, due to budget constraints and arms control treaties, many of its ships became increasingly obsolescent.

In 1936, the buildup began again; by 1939, with the emergence of war in Europe, a force increase of 90,000 was authorized. Beginning in 1940, the army began a (relatively) massive expansion to 1,500,000 men, primarily achieved through a reinstated draft. New equipment began to be procured, but this was still a fairly small army for a nation facing an imminent two-front war against fully mobilized opponents.

Mobilization reached fever pitch upon outbreak of war. For two years, the military expanded basically as fast as men and equipment could be procured. By 1944, manpower limits began to be felt, and it was decided to settle on an an ultimate authorized size of 10,500,000 in the Army, Navy, and Marine Corps. This was the apogee of American military strength. Never before or since was such strength mustered.

Inevitably, the military was drawn down, especially the Army and Marine Corps, while the newly formed Air Force and Navy remained quite strong. By 1950, the Army was down to approximately 600,000 men - with, of course, a large, modern Navy and Air Force of approximately 411,000 and 380,000, respectively. A minor expansion occurred due to the Korean War, and from 1955 to 1975 the Army would hover at around one million men, ramping up slightly for Vietnam. This does not seem particularly impressive until it is considered that the traditional powers of Europe increasingly demobilized; UK military strength, which had peaked at nearly five million during WW2, was down to something less than a million in the 1950s, and less than one half-million in the 1960s and 1970s.

TL;DR: The US military's peacetime strength was laughably weak until WW2, and became dominant in the post-war period due to the general demilitarization of most of the world's traditional powers.