How do I manage people who are older than me?

You are younger than most of the people you lead, and you feel it in every room, that quiet sense you must prove you belong before anyone will follow. So you over-prepare and over-explain to cover an age gap that, as you say, no one has actually raised out loud. The pressure is real, but notice where most of it is coming from. It is coming from you. People do not follow a leader because of age. They follow because they feel respected, because decisions are fair, and because the person in charge is steady and honest. Your experienced team members likely care far less about your years than about whether you listen to them and have their backs. The over-explaining can actually work against you, signaling the very insecurity you are trying to hide. Calm confidence reads as authority. Over-justifying reads as doubt. Try trusting your people instead of trying to out-prove them. Ask an older team member for their view on a real decision and genuinely use it. Say less in the next meeting, and let a clear, steady presence do the work that all that preparation was trying to do. You earned this role. You do not have to keep re-earning it every hour. Lead as someone who belongs here, because you do.