Eastern Syria (CNN) The unmistakable sound of automatic machine gunfire pierced the early morning, sometime before 7 am. While it was not unusual to wake up to the cacophony of war -- be it coalition bombing from airstrikes or gunfire -- this was different.

For days, I'd been traveling with fighters from the US-backed Syrian Democratic Forces (SDF), who launched a last offensive to oust ISIS from its only remaining enclave in Syria over the weekend.

Since sundown on Saturday, coalition airstrikes had been pounding the last remnants of the jihadi group's so-called "caliphate." Now we were holed up in a war-torn building just a kilometer from the town SDF fighters were working to liberate: Baghouz Al-Fawqani.

We scrambled to the rooftop for a better vantage point. There was little to see, save for explosions in the distance which appeared to be a combination of airstrikes and shelling from the US, British and French positions toward the town. As we watched, we heard rounds coming in our direction. Zing came one, then another, then another.

On this cold winter morning, ISIS were taking advantage of the mist at daybreak to launch a counterattack. We ducked behind a wall as bullets continued to fly over our heads. The morning before, coalition airstrikes had suppressed any possible assaults. But now, the gunfire appeared to be intensifying.

The soldiers around us became agitated by the onslaught. One of them got on a walkie-talkie for more information about the assault. Then a huge blast rocked somewhere nearby and gray smoke started billowing from the side of our building.

Retreating to the building's stairwell, it occurred to us that we might be in danger of being overrun by ISIS -- one of their tactics is to encircle during an attack rather than come from the front.

We weighed our options and decided it was time to move back. We pulled back about five kilometers to another house in a safer area to reassess, eat breakfast and drink tea. As we shared a meal with the soldiers, it was clear that their earlier confidence of a quick and easy battle was shaken.

Until Monday morning, the operation had seemed to be working on schedule. The battle's first 24 hours saw little resistance from ISIS and buoyed the confidence of the SDF fighters we traveled with. Commanders had told us over tea that they might take the town by Monday or Tuesday.

But the morning's events had brought a harsh truth home: ISIS was not going to give up easily, and its fighters certainly weren't going to be defeated quickly.

Later in the day, we came across an assembly point where people fleeing the town are checked, given medical assistance and food and water. It's here that men are separated from women and questioned to identify any potential ISIS members or sympathizers.

Most remarkable was the sheer number of residents escaping Baghouz Al-Fawqani. I counted 21 trucks loaded with people destined for refugee camps. A local official managing the convoy estimated that about 700 people were leaving.

SDF officials had been telling us for days that the total number of people in Baghouz Al-Fawqani was only about 1,500 residents, with 500 ISIS fighters -- but clearly that number is much bigger. SDF spokesman Mustrafa Belli later told me that they had underestimated the number of civilians and that they likely numbered the thousands.

One of the fleeing civilians, an older woman, told me that the town's residents were being used as human shields. A man who had fled told me the entire town had been shelled and little shelter remained. Another said those that remained were resorting to eating the grain for their livestock.

When I asked about ISIS, one resident described fighters from all over the globe -- some appeared to be European while others looked to be Russian and Chechen, as well as others from Central Asia, he said.

As I spoke with these exhausted and disoriented townspeople, I thought back to US President Trump's remark that he hoped to announce a victory against ISIS in Syria, in the coming days.

His statement may have galvanized SDF commanders as their last offensive began. But the reality is that this is not an operation that works on a timetable. It will take as long as necessary -- maybe even weeks.

And as fighting intensifies and soldiers push forward, nobody on the ground is making predictions anymore.