What is the best way to lead a new soldier who is uncertain if they even want to be in the army?

Tell them that they are stuck in the Army for their enlistment and they need to make the best of it. Find something they are good at and let them do it.

My initial response would be to assume he's having a rough day and tell him, "Tough tutus. Get back to work." Realizing, from two perspectives, the situation merits observation and close, but as surreptitious as possible, monitoring. In fairly short order.
Is he sincere? Risk of AWOL....or worse.... And is he poisoning other minds with his new attitude?
Either way, if his attitude doesn't adjust, and regardless of what kind of soldier he is, I have to draw him a little close for some appropriate but friendly informal counselling for a few days until I figure out 'where he is coming from' and determine whether he's worth the effort to try and save. 'Cuz this is gonna steal valuable time from me.
At some point fairly early on I have notify my boss. That could go either way. I still gotta do it.
If separation is the final answer; can he still perform while being processed?; or, does the 1SG need a clerk?; or maybe Bn needs a runner/coffee maker.
Drawing these thing out isn't good. In my day, the Army was less than expeditious about such matters.

Well i guess you make him strong. Every shit detail there is and make some up. New generation. The Army is easy do what your told lead from the front or the front leaning position.

Sp4 Byron Skinner…I guess this problem is as old as the Army itself…Back 50 years ago we had about half of the Army was conscripted, so this problem was not uncommon…If you are in a combat arms platoon and are in a deployable status there is no choice get rid of the solder as quickly as you can…This really is a life or death issue…In the unit I was in if a line Platoon Leader wanted to get rid of a soldier with this problem it was best for the soldier and the Platoon to transfer the problem soldier to HQ Co. before the members of the platoon took matters in their own hands…this was the era of the infamous blanket party in the latrine…These blanket parties really did happen and soldiers really did get hurt..The SOP for the platoon was nobody knew who did it or what happened…Myself if I had an issue with somebody I took care of it myself.

Had one who said the same while in the shot line waiting deployment to desert storm. He quickly got over after he got it said. Turned out to be a good troop.

My perspective might not be the most ideal example but I believe it deserves airing.
I enlisted less than a year after I lost my father. My duty assignment after OSUT was not a pleasant experience. I had a hard time fitting in, a problem made worse by a fellow OSUT class member who ingratituded himself to the "in" crowd with relative ease, and missed no opportunity to make my life miserable. I wasn't a drinker which kept me out of the most immediate Avenue to socialize or fit in. I never once was given even the most rudimentary sense that anyone cared or that my contribution was valued in any way. Top all of that off with dealing with some other personal issues predating my time in uniform that made trusting people difficult (read as impossible!) and long story short my time on active duty was brief with at the time I was discharged no chance of ever enlisting again.
Fast forward 9 years. I now had an amazing woman in my life who encouraged and pushed me to accept God into my life, confront my demons and further my education. She gave me the courage to pursue a waiver to join the National Guard. I now had the opportunity to be the sort of senior enlisted peer and eventually leader that I wished I peyote when I was on active duty. I wasn't a wishy washy pushover, but I didn't go out of my way to treat people like shit either. I led by example as best as I could and I called out people who mistreated junior enlisted simply because they thought they could for their lack of professionalism.
Was I liked by everyone? No. Did the people who served under me and to whom I reported to know where they stood with me and that I was 100% dedicated to the people who I served with? Absolutely.

You resell the Army to that trooper!!! Tanks best job in the world.

Plenty of Soldiers have told me they were done with the Army, some of it stemmed from previous poor leadership, some felt they weren't getting any career progression and some just didn't want to put up with the long hours. Each case had a story, some I was able to change their minds and they reenlisted, others, well it was just time for them to go before they become an drain on the good order and morale of the unit. Mid-career Soldiers deserve a little more consideration and understanding why they want to leave. In each case, it was important to do some problem solving. As leaders it is important that we really know our Soldiers, dig deep into underlying causes of Soldier issues. Yes it takes time, more time than we have in most cases. But we do it. We do it because its in our creed to know our Soldiers and its our job to build effective teams, to know the strengths and weakness in the ranks. Whether you are dealing with a first-termer or a mid-career Soldier. Your leadership, guidance, mentorship and professionalism will always guide a leader to do what is best for the unit and the Army. Talent management happens at all levels of leadership.

"I don't wanna play Army anymore" is not uncertainty. they want our, push them out. Separate them from the rest of the troops, start separation paperwork on them, give them busy work to do, extra duties, drag out the separation. Make sure they get an administrative separation on their paperwork. They want out, give it too them. But show them there are consiquences.

I was in for 30 years ... I had a 100% Retention Rate. I am not certain why and frankly, I did not realize it until I was asked to fill out a questionnaire at the end of my career concerning retention. I tried to treat my Sailors with respect. I never asked them to do anything I wouldn't do or had not already done. When I was still a CPO and did retention interviews, I asked what their plans were and discussed the realism of whatever they had in mind. I got a few doozies, but no one ever got out my watch.