There has never been any legal compulsion to 'volunteer' for national service.
Like everything else in law. It's all about contract.
Typically, when one reports for a so-called mandatory military induction, one is told to line up on a yellow line painted on the floor, along with all of the other new recruits. A Recruiting Officer will then tell all those joining to take one step forward. Everyone who does take one step forward just 'volunteered'. They are all then led through an Oath of Allegiance into national service.
How not to volunteer? Don't take the step forward or the oath that immediately follows.
Be prepared for intense threats and bullying from the officers, but know that they cannot make you contract with them on their terms. Rely on questions and the 3 useful tools.
When they tell you to do anything, you can ask are they ordering you. If they say Yes, you can ask by what authority. If they say by the authority of the U.S. Government or some such thing, you can ask: "Which clause of the Constitution gives you, a military officer, the right to order me, a civilian?"
Another thing you can say is: "Am I free to go?" If the recruiter says No, then you can ask: "Am I under arrest? Am I your prisoner? Am I kidnapped? If you ask the question three times and don't get a yes or no, you can then say: "Well I must be free to go, because I asked you three times and you won't tell me I'm not." Then you can slowly turn around and leave. If he or they keep trying to interact you can just keep repeating the question. Eventually, as long as you do not contract with them otherwise, they have to let you go. See: How to Avoid the Draft or National Service; again.