But after two decades of war in the lawless Horn of Africa country, nothing can be taken for granted.
One indication that the Islamists, known as al-Shabaab, are having a hard time is they have launched a major recruiting drive to counter pressure by TFG forces along the southern border with Kenya.
"We urge Somalis, in particular military officers from previous governments, to take up weapons and support al-Shabaab's counterattack," declared one of the insurgents' key leaders, Sheik Mukhtar Robow Mansur.
Details of the fighting outside Mogadishu, Somalia's war-battered seaside capital, are sketchy but scores of people have been reported killed since the TFG offensive began Feb. 23 after months of preparation.
According to a variety of sources, including Western relief agencies, the government push has made sizeable gains in Mogadishu and in the south and center of the country.
These are all al-Shabaab bastions but from the various accounts the sheer weight of the TFG offensive by some 17,000 troops has retaken several districts of Mogadishu, pushing outward from the tiny enclave around the port that was all the TFG had controlled for the last couple of years.
The government forces are spearheaded by an 8,000-strong African Union peacekeeping force known as Amisom, which has considerable firepower and artillery.
Government troops, many of them recently trained in Kenya under U.S.-funded programs, total around 9,000 men. But they are poorly led and badly equipped.
"If it wasn't for Amisom and the Ethiopians, the TFG would be in bad shape," a Western observer commented.
Ethiopia, a U.S. ally, has provided armor and artillery support for TFG forces along part of its border abutting western Somalia and in the south along the frontier with Kenya, a TFG supporter.
The Ethiopians have done this before. In 2006, a large Ethiopian force with tanks and air support invaded to topple a short-lived Islamist regime in Mogadishu and install the Western-backed TFG.
The Ethiopians, who had been tacitly supported by the Americans who sought to crush the Islamists linked to al-Qaida, withdrew in 2009.
Heavily armed Ethiopian troops were reported to have encircled a large force of al-Shabaab in the town of Belet Weyne, near the Ethiopian border, and were pounded them with artillery fire.
The government has also been aided by fighters of the Ahlu Sunna Wal Jama'a militia in the fighting on the border between the Kenyan town Mandera and the Ethiopian frontier town of Dollow.
In the Mogadishu fighting, the government forces punched out of their enclave, covered by heavy shellfire from the Amisom guns, and overran several blocks of the city.
They reoccupied the Defense Ministry building, which al-Shabaab had used as a forward headquarters.
The troops also seized an elaborate mile-long trench and tunnel network the Islamists used to infiltrate fighters into government-held areas and move supplies and ammunition.
Despite the TFG's gains, the shaky, corruption-riddled government of President Sheik Sharif Sheik Ahmed may not be able to hold on to them. It has invariably lost ground taken from al-Shabaab in the past.
The TFG is also riddled by in-fighting, reflecting the constant conflict between Somalia's clans that has also infected al-Shabaab in the past.
The offensive was only able to go ahead after the TFG agreed to pay its troops several months' back pay after officials pocketed the money themselves, forcing troops to sell their weapons -- often to the enemy.
The timing of the offensive was undoubtedly linked to the impending expiration of the TFG's mandate in August and the possibility it might be replaced with a more effective administration with wider representation.
The mandate can only be extended with the approval of the international community that established the TFG.
The Somali Parliament sought to pre-empt the mandate question by unilaterally voting to extend the TFG's term for another three years. The Americans said that "risks strengthening al-Shabaab."
The International Crisis Group in Brussels was more forthright, saying, "The decision to prop up the TFG at all costs has been a failure."
But, it stressed: "If the right political conditions and strategy are put into place, it would be possible to rapidly re-establish peace and stability."