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.

SPC, Sometimes it is impossable to do. There are going to be people that think it's a way to take your money and you don't actually own the account. At my civilian job after i retired I was the older dude. I have the younger prople ask a lot of questions and some were about the 401k's the company had. I tried for about 3 years to get one man to sign up but he never did. I quit after he told me that was the same thing his Dad told him. But I did get some to raise what they put in. When I retired I hava a man tell me Thank You for making him sign up for the 401k. But I didn't make him, however i did feel good about helping someone.

Like SGM Quick said, I would also encourage them to look past today.
I would also let soldiers know that there are other options outside of the Military. Plenty of programs that can match and give better interest rates. I currently use Primerica Mutual Funds.

http://shareholder.primerica.com/public/shareholder/mutual_fund_disc.html

The amount you have a savings/retirement should double every 7 years.

I would brief them on what usually occurs; you wind up retiring with Social Security which in one leg of your retirement planning, and the EXTREMELY low cost of investing in TSP, and what they COULD have at retirement for income based on past performance of TSP/mutual funds. It's difficult to get thru to our young warfighters as they think they are invincible and will live forever. Start saving early, get in the habit, increase contribution at every pay raise, COLA, promotion, bonus and it will be painless. I have been saving in TSP/Mutual Funds since 2005 and I have hit $200K. I only have 5-7 more years to grow my nest egg as I am 58. So I am looking at four legs in in retirement; Military Retirement, Govt retirement, Social Security and 401K (TSP) distribution.

Maybe information on the program could be included in any information provided to SMs on the newly instituted retirement system. Without command guidance or involvement it is unlikely many SM will ever hear about the TSP or possibly the retirement program. There may be mandatory briefings on the new retirement program. A simple printed brochure on TSP could be included with anything on the retirement program. Does anyone have any idea how information on either program is being provided to SMs today.
Here is one of the brochures available on line to SMs; getting this info to the rear rank pvt is the hard part. https://www.tsp.gov/PDF/formspubs/tsplf36.pdf