Well, there’s a remote island that belongs to Alaska that’s about two miles away from a remote island that belongs to Russia. You can swim across that.
en.wikipedia.org/wiki/Diomede_Islands
I mean, I’m sure that Russia can get forces across that. They’ve got a military base on their little island, and we’ve got a small Native American village on our little island.
But then you’ve planted some number of forces on a strategically-irrelevant island in the Pacific. You’ve blown your largest advantage, surprise, and you’ve dumped however many people there, with a supply line that dictates that you need to support them by having ships sail up, while you just kicked off a war with a country with a much larger navy and air force.
And it’s not much of a springboard to a beachhead that you can use for land-based logistics, because there’s no infrastructure up there.
en.wikipedia.org/wiki/Bering_Strait_crossing
The Russian side of the strait, in particular, is severely lacking in infrastructure. No railways exist for over 2,800 kilometers (1,700 mi) in any direction from the strait.[24]
The nearest major connecting highway is the M56 Kolyma Highway, which is currently unpaved and around 2,000 kilometers (1,200 mi) from the strait.[25] However, by 2042, the Anadyr Highway is expected to be completed connecting Ola and Anadyr, which is only about 600 kilometers (370 mi) from the strait.[26]
On the U.S. side, an estimated 1,200 kilometers (750 mi) of highways or railroads would have to be built around Norton Sound, through a pass along the Unalakleet River, and along the Yukon River to connect to Manley Hot Springs Road – in other words, a route similar to that of the Iditarod Trail Race. A project to connect Nome, 100 miles (160 km) from the strait, to the rest of Alaska by a paved highway (part of Alaska Route 2) has been proposed by the Alaskan state government, although the very high cost ($2.3 to $2.7 billion, about $5 million per mile, or $3 million per kilometer) has so far prevented construction.[27]
In 2016, the Alaskan road network was extended westwards by 50 miles (80 km) to Tanana, 460 miles (740 km) from the strait, by building a fairly simple road. The Alaska Department of Transportation & Public Facilities project was supported by local indigenous groups such as the Tanana Tribal Council.[28]