Age at Marriage
A critical way the shortage of women is solved is by having women marry very young but men marry when they are fairly old.
Next: Advantages of Polygyny
You can think of this mathematically: imagine that all men get married at age 30 and die at age 60. They then have 30 years of marriage possible. Imagine that all women get married at age 15 and die at age 60. They then have 45 years of marriage possible. So, you don't actually need extra women to produce sufficient wives, you just need extra marriage years. On the one hand, there are various problems for this idea, customs like the levirate (which we will talk about later) get in the way. In some places, women are not permitted remarriage. However, the principle does generally work.
So, the general effect of polygyny is to push the average age of first marriage apart, with men marrying fairly late (late 20s early 30s) and women marrying as early as their young teens. This difference is often exacerbated by disparities in wealth and power. Since marriage is a system of alliance (more on this later too) families may wish to ally with the wealthy and powerful and these are generally older men. Older men with wealth and power might also wish young brides. So, it is not terribly unusual for men in their 50s and 60s to marry women in their teens. However, of course these men were likely first married in their 20s or very early 30s, so new young brides enter their families as junior wives.