A study by the RAND Corporation last year estimated that 2,450 of the 1.2 million active-duty members of the military are transgender, and that every year an estimated 65 would seek to transition to the other gender.

The study found that transitions — including hormone therapy and medical procedures like surgery — would cost the Pentagon $2.9 million to $4.2 million a year, a tiny fraction of its $610 billion budget. Some transgender troops are already taking advantage of the medical benefits.

Among them is Blake Dremann, 35, an active-duty Navy officer stationed at the Pentagon. He began his transition to male from female in 2013, he said, “well before the policy was remotely talked about.” Since then, he has gone through a double mastectomy, while assigned to a submarine, and has had chest reconstruction surgery, paid for by the taxpayers under the new policy.

The taxpayers have also financed Ms. Dosh’s education; a West Point degree is worth more than $225,000, according to the academy’s website.

“That’s a big investment for the military to make on somebody, when they’re just going to say, ‘Go get a civilian job,’” said Matt Thorn, executive director of OutServe, an organization that provides legal services for lesbian, gay, bisexual and transgender members of the military. His organization is pressing Pentagon officials to reconsider their position.

Ms. Dosh, who will graduate on Saturday, said she “came out to myself” in April of last year, when she was a junior.

In June, the defense secretary at the time, Ashton B. Carter, announced that the ban would be lifted; in August, at the outset of her senior year, Ms. Dosh saw a behavioral health specialist at West Point, who gave her a diagnosis of gender dysphoria — the first step toward a transition.