How can I enlist in the U.S. marines after the EB-5 conditional green card expires?

You are still considered a permanent resident as the I-829 is pending, but the way other government agencies may look at your position may depend on their specific policies.

You should be able to enlist while your I-829 is pending because your status will be automatically extended for 1 year upon the filing of I-829.

When you file for the removal of lawful permanent residence status (I-829), you are accorded an automatic extension of status for one year. If your petition is not approved within that year (which is likely), you can obtain extensions at the local USCIS district office. In either case, you would be eligible to enlist.

Once you obtain EB-5 conditional resident status you should be eligible to enlist in the U.S. military since you are a lawful permanent resident of the United States. While your conditional green card expires, once you timely file your I-829 petition even though, as you say, it takes a number of months for same to be adjudicated and your unconditional lawful permanent residency is approved, you are still a valid legal resident during that time. It is true that the card itself is issued for 10 years, but that is just the validity date of the card. You become a permanent resident without any conditions. But the important point is you maintain your residency throughout that period of time. In terms of your ability to enlist with your current paperwork, I would simply proceed to apply to the U.S. marines, showing them what you have and insisting that you are a permanent resident of the United States and if questioned, you can say that the conditions will be removed in due course.

The I-829 will take closer to two years, but you should have gotten a receipt extending your green card for another year. The military hotline may also be able to help you accelerate this and/or naturalize.

As soon as you file the I-829, that automatically extends the green card for one year; thereafter you can get extension stamps, or temporary green card stamps by going to your local immigration office. As long as the I-829 is pending, you are a permanent resident and will have no trouble joining the marines since you are and will be a permanent resident. The I-829 is taking almost two years to adjudicate.

Yes, you can enlist while waiting for removal of condition from your status.