Today hundreds of missiles in southeast China are within range of Taiwan, the self-governing democratic island supported by the United States. Missiles at other sites can hit Japan and India, and there are Chinese missiles that can strike the United States territory of Guam and other potential targets in what American strategists call the second-island chain.

“Unilateral constraint was a losing proposition: China developed the world’s foremost force of missiles precisely within the ranges that I.N.F. would prohibit,” said Andrew Erickson, a professor of strategy at the United States Naval War College. “So this increasingly antiquated treaty had no future.”

Until now, the Trump administration has held off on testing new missiles that would violate the treaty; under its terms, even testing is prohibited. But that stricture lifts on Friday, and the first test of new American intermediate-range missiles is likely to begin within weeks, according to American officials familiar with the Pentagon’s plans.

The first, perhaps as early as this month, is expected to be a test of a version of a common, sea-launched cruise missile, the Tomahawk. It would be modified to be fired from the ground. (The treaty prohibited intermediate-range ground-launched missiles, but not missiles launched from ships or airplanes.) If successful, officials say, the first ground-launched cruise missiles could be deployed within 18 months or so — if the United States can find a country willing to house them.

That would be followed by a test of a new mobile, ground-launched ballistic missile with a range of 1,800 to 2,500 miles, before the end of the year. But that would be an entirely new missile, and it is not likely to be deployed for another five years or so — meaning the very end of the Trump presidency, if he is re-elected.

But the question is where to deploy them. “I don’t think the Europeans want to host them,” Gary Samore, the director of the Crown Center for Middle East Studies at Brandeis University and the chief nuclear strategist at the National Security Council under Mr. Obama, said on Thursday. In Asia, he noted, the two countries where it would make most sense to deploy the missiles would be Japan and South Korea, though any move to put the missiles there could infuriate China.

“The real question is where and whether or not there would be pushback,” said Bonnie S. Glaser, a senior adviser for Asia at the Center for Strategic and International Studies. “The most obvious place is someplace in Japan.”