A second American contingent, due in April, is to be positioned in eastern Poland in the so-called Suwalki Gap, considered the likeliest path for a Russian land invasion, although such an invasion is considered unlikely.

But here in Eastern Europe, Polish and other regional leaders are less certain, wondering whether those future troops will show up after Mr. Trump assumes office and, if they do, whether they will be based in the east, as promised.

And that does not take into account concerns about other promised American and NATO initiatives to reassure the anxious East, including an American missile shield to be built in Poland, mirroring one already in place in Romania, and the opening of forward supply depots throughout the region where NATO armaments could be stored to make rapid deployment possible in the event of an invasion.

“I would say the forward positioning will not happen and, if there is any, it will be in the west of Poland,” Mr. Zaborowski said. “Trump will come to some sort of agreement with Putin about keeping troop levels as low as possible, keeping real deterrent capability as low as possible and keeping the troops in the west of Poland instead of the east.”

Mr. Stavridis said he expected the troop deployments to take place as scheduled, but suspected that the new administration’s desire for a Moscow deal will lead to some horse-trading, perhaps involving that promised missile shield.

The nomination of Gen. James N. Mattis, a strong proponent of NATO, as Mr. Trump’s secretary of defense does give Eastern Europeans more confidence.

“I would be very surprised if General Mattis backs off from this,” said Thomas Donnelly, co-director of the Marilyn Ware Center for Security Studies at the American Enterprise Institute. “This deployment may not be everything you would like, but it’s a real improvement. It’s definitely more than half a loaf.”