Your question is premised on some incorrect assumptions:
Casualties were not that high. The U.S. Army enlisted over 11 million men and suffered less than 500,000 killed and MIA, only a bit more wounded (but many of whom returned to service). Overall percentage killed was 2.2%. Yes, the U.S. military is known for its long tail, but even for the pointy end of the sword the percentage killed over the entire 4 years is certainly much less than 10%.
Enlisted men aren't promoted beyond Corporal based on length of service. Leadership roles go to leaders, and in each batch of recruits the potential leaders would be promoted to Corporal early on. Barring truly exceptional battlefield performance, future sergeants are promoted, based on merit, exclusively from these early leaders.
Most sergeants, and the best sergeants, are considerably older than both their men and their lieutenants. Long experience, both in life and in service, is a prerequisite for a good sergeant. Only very exceptional men between the ages of 18 and 25 can hope to possess the maturity looked for in a sergeant. This means that throughout the four years of the war, sergeants were mostly drawn from the older recruits and the existing cadres of corporals in December 1941.
Sergeants must be respected by their lieutenants, who will usually be several to many years younger. The most foolish man in the army is a Second Lieutenant who won't request, and take, the advice of his lead sergeant. Again, this respect is given based on both the greater combat/military experience of the sergeant, and his overall greater maturity. Age matters.
Sergeants are technical experts; the experts in each platoon and company. It is not necessary that he be the very best, but he must be amongst the three or four best, for every single task that his unit members must perform. A primary responsibility at all times is the instruction of his men into better soldiers. This requires intelligence, character, aptitude, empathy, and maturity.
So if you are wondering what sort of new recruit in Spring 1942 might get promoted to Sergeant by sometime in 1944:
- already aged late twenties or early thirties
- amongst the smartest few men of his company;
- amongst the most consciencious few men of his company;
- stands out across the entire range of company activities as very competent; and
- stands out as a leader and mentor in bootcamp and gets an early promotion to Corporal.
Note that the biggest percentage, and thus most difficult, growth in the size of the U.S. Army had already occurred by Pearl Harbour: roughly eight-fold from just 184k in late 1939 to 1,142k in December 1941. It would double and a bit in 1942, double and a bit again in 1943, and only increase by another 14% in 1944. Most of the senior sergeants and warrant officers required by 1945 were probably already in uniform by late '41 or early '42.