How should we influence new soldiers to contribute towards their TSP?

Encourage them to look past today...

They need to learn the hard way just like the rest of us did. So let them go out and blow their whole deployment pay on a Corvette at 16% interest that the pregnant stripper they just married talked them into buying.

When I joined the Navy, my base pay was $77.10, even then I took out a savings bond per month that took half my pay at that time. It continued for the next four years when I reenlisted as an E-5. It only resulted in a couple thousand dollars, but set in motion a trend for saving for retirement that I used until I finally retired. Anything that offers tax deferred compensation or matching funds should be taken as fast as possible, if you can afford it, go Roth and contribute to the max that is legal. As far as educating our young enlistees, that is a tough one, most want everything now, just as they did before becoming a service member.