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NEVSKE, Ukraine — In a tiny village in eastern Ukraine at the epicenter of the next phase of the war, Lyudmila Degtyaryova measures the Russian advance by listening to the boom of incoming artillery shells.

There are more and more of them now. And they are coming more frequently, as Russian troops grind their way forward.

“You should see the fireworks here,” said Ms. Degtyaryova, 61, as the sounds of artillery howled all around. “It is like New Year’s.”

Russia’s military is preparing to launch a new offensive that could soon swallow Ms. Degtyaryova’s village of Nevske, and perhaps much more in the eastern Ukrainian region known as the Donbas. But already the impact of Russia’s stepped-up assault is being felt in the towns and villages along the hundreds of miles of undulating eastern front.

Exhausted Ukrainian troops complain they are already outnumbered and outgunned, even before Russia has committed the bulk of its roughly 200,000 newly mobilized soldiers. And doctors at hospitals speak of mounting losses as they struggle to care for fighters with gruesome injuries.

The civilians standing in the way of Russia’s planned advance once again face the agonizing decision of whether to leave or to stay and wait out the coming calamity. This area in the northern Donbas was among the last to be liberated in a Ukrainian blitz offensive last fall that raised hopes among local residents that their months of trauma were over.

But the war has come back. Two weeks ago, a Russian shell landed in Ms. Degtyaryova’s yard, and as she contemplated her future over the weekend, the remains of her barn still smoldered.

She has rabbits, ducks and three pregnant cows to care for. A chicken, its feathers partly burned off in the recent strike, lay recovering in a bed of hay, its small injured foot in a homemade cast.

If the Russians come back, she lamented, she’ll have to flee.

“I’ve started to pack my things, if I’m being honest,” she said. “The soldiers will cover my back and I will leave. I’ll let my cows out and I’ll go. I don’t want to go back there.”

When and where the new offensive will begin in earnest is still unclear, but Ukrainian officials are gravely concerned. Ukraine’s military defied dire assessments before the war, thwarting Russia’s early efforts to seize the capital, Kyiv, and eventually driving Russian forces back in the northeast and south.

But the Russian military just keeps coming. Right now, the newly mobilized troops are finishing their training and entering the field; the forces include as many soldiers as took part in the initial invasion last year.

They could be ready to fight in as little as two weeks, said Serhiy Haidai, the governor of the Luhansk Region, which includes Nevske — much sooner than new Western weapons, including tanks and heavy armored fighting vehicles, are expected to arrive in Ukraine.

“There are so many,” Mr. Haidai said of the new recruits. “These are not professional soldiers, but it is still 200,000 people who are shooting in our direction.”

Russia is expected to punch hard, looking to reverse nearly a year of cascading failure. While a renewed attack on Kyiv is now considered improbable, Russian forces will likely try to recover territories they lost last fall. as well as take full control of the Donbas, a key objective of Russia’s president, Vladimir V. Putin.

Military analysts say that one likely scenario would be for Russian forces to swing down from the north and up from the south in an arc, creating a large claw that would cut off Ukrainian supply lines running east and west. That would put villages like Nevske in the direct path of Russia’s likely advance.

For locals it would be a disaster. Out here at the far edge of Ukraine’s offensive, people have not experienced the fruits of liberation the way Ukrainians farther west have. There is still no power or water and the fighting has never subsided. Fields of black unharvested sunflowers are pocked with snow-filled craters, and the area is littered with burned out tanks and unexploded ordinance and mines that frequently kill livestock. Passing through the region, one occasionally comes across their frozen bodies or bones.

In Makiivka, just north of Nevske, five of Ruslan Vasilchenko’s cows have been killed, and those that remain were huddled on a recent day in a tiny barn that had been spackled with shrapnel. There was a burned tank in his garden and two destroyed cars in his courtyard. He said he expected things would get much worse soon.

“Over the last few days, the soldiers have come by to tell us not to leave our homes,” he said.

The first stages of the Russian offensive have already begun. Ukrainian troops say that Bakhmut, an eastern Ukrainian city that Russian forces have been trying to seize since the summer, is likely to fall soon. Elsewhere, Russian forces are advancing in small groups and probing the front lines looking for Ukrainian weaknesses.

The efforts are already straining Ukraine’s military, which is worn out by nearly 12 months of heavy fighting.

Troops say they have tanks and artillery pieces, but not enough of either, and have far less ammunition than their adversaries. Russian forces have also started to field more sophisticated weaponry, like the T-90 tank, which is equipped with technology capable of detecting the targeting systems of anti-tank weapons like the American made Javelins, limiting their effectiveness.

Mostly, though, the challenge comes down to numbers.

“It’s particularly difficult when you have 50 guys and they have 300,” said a 35-year-old infantry soldier named Pavlo, who was struck in the eye with a piece of shrapnel from a rocket-propelled grenade near Bakhmut. “You take them out and they keep coming and coming. There are so many.”

Losses among Ukrainian forces have been severe. Troops in a volunteer contingent called the Carpathian Sich, positioned near Nevske, said that some 30 fighters from their group had died in recent weeks, and soldiers said, only partly in jest, that just about everyone has a concussion.

“It’s winter and the positions are open; there’s nowhere to hide,” said a soldier from the unit with the call sign Rusin.

At one frontline hospital in the Donbas, the morgue was packed with the bodies of Ukrainian soldiers in white plastic bags. In another hospital, stretchers with wounded troops covered in gold foil thermal blankets crowded the corridors, and a steady stream of ambulances arrived from the front nearly all day long.

A military surgeon at that hospital, Myroslav Dubenko, 36, scrolled through photographs of soldiers with ghastly injuries: a lower jaw blasted off, half of a face missing. One soldier was rushed in with his throat sliced open from ear to ear. Dr. Dubenko was able to quickly repair the damage, and the soldier survived.

“In civilian life, you know that no matter how horrible your shift is, it will end sooner or later,” Dr. Dubenko said. “Here, you never know when it will end.”

It not just the influx of soldiers that is consuming doctors; civilians, too, are frequent victims of Russian attacks. For Andriy Drobnytsky, a 27-year-old military doctor, this is part of a deliberate strategy of overwhelming Ukraine’s military hospitals. Last week, a retired prison guard was rushed into the military hospital where Dr. Drobnytsky is deployed, his hand blown apart by a mortar shell that exploded while he was gathering firewood. Dr. Drobnytsky assisted in sewing his hand back together, probably saving his index finger.

“If there are lots of victims, we’ll get distracted by them,” he said. “You just can’t abandon them, right?”

Whether Russia will be able to capitalize on its strength in numbers is an open question. Russian soldiers, according to Ukrainian and Western assessments, are dying in far greater numbers. American officials now estimate the number of Russian troops wounded and killed to be approaching 200,000, an astounding casualty rate.

In his sleeping quarters at a base near Bakhmut, a soldier with the call sign Badger pulled out a cloth bag and dumped its contents onto a cot. Inside were half a dozen knives — one with a hilt made from a deer’s hoof — trophies he said he had taken from the bodies of dead Russian soldiers.

“We also have losses, but they have huge losses,” Badger said. “We’ve wasted them all in huge numbers.”

Back near Nevske, soldiers from the Carpathian Sich said they had enough ammunition to hang on for now. One soldier, with the call sign Diesel, showed videos on his phone of the bodies of Russian troops he had killed when they came too close.

As they have since the beginning of the war, the Russians continue to make stupid mistakes, he said. From one dead officer, Diesel said, he took a tablet computer without an access code that had the coordinates of all of their mines and snipers.

In a video he recorded from the front, Diesel approaches a body lying in the snow, his rifle muzzle trained on the Russian’s head.

“Hello,” he whispers after determining the man was dead. “Did you sleep well?”