You can think that, but they actually became a critical voting and marketing demo in the 60s when they hit adulthood.
The very first boomers didn't turn 21 until 1967. Then, as now, people in their early 20s were not a significant voting bloc. Voting age was lowered to 18 in 1971, which added more Boomers to the voter rolls, but they weren't a large cohort of voters until all the 50s kids were voting, which took until 1978.
Also, a generation doesn't have real power until they have money, and you just don't have much money until you're about 40, maybe mid to late 30s if you're lucky. The first Boomers turned 40 in 1986, and the last Boomers turned 40 in the 2000s, depending on where you say the cutoff is. So that makes the period of maximum boomer cultural influence the 80s and 90s. Most people just think Silents are Boomers, or they think the 60s radicals were Boomers because their Boomer parents loved their music as teenagers. David Lee Roth is a Boomer. David Crosby is a Silent.
The median Boomer was born in 1955. He was 8 years old when Kennedy was shot and 14 when Neil Armstrong landed on the moon, same year as Woodstock. He turn 18 years old the year Nixon ended the Vietnam war in 1973. He graduated college in 1977. He probably had his first kid in 1980, at the age of 25. In 1995, at age 40, he made it to middle management in a large company, divorced his wife, and remarried someone 10 years younger. In 2003, he was 48 and a little concerned about his son coming home safely from Iraq. The '08 crash freaked him out because, at age 53, retirement was looming. He then finally did retire in 2020.
You essentially have your entire concept of Boomers shifted backward by about 10-15 years and are mostly thinking of Silents.