Military commanders appointed Sharaa interim president weeks after Islamist-led rebel forces overran Damascus.
His nomination has been welcomed by key regional players Egypt, Qatar, Turkey and Saudi Arabia.
Syrians are "now fully dependant" on the intentions of the new authorities over the future of their country, said Damascus-based lawyer Ezzedine al-Rayeq.
"Will they really take the country towards democracy, human rights?" he asked.
Sharaa led the Islamist Hayat Tahrir al-Sham group, which spearheaded the rebel offensive that toppled Assad on December 8.
The group and other factions have been dissolved, with fighters set to be integrated into a future national force.
Sharaa has now traded his fatigues for a suit and a tie.
In his first address as president Thursday, he vowed to "form a broad transitional government, representative of Syria's diversity" that will "build the institutions of a new Syria" and work towards "free and transparent elections".
Sharaa had already been acting as the country's leader before Wednesday's appointment, which followed a closed-door meeting with faction leaders who backed the overthrow of Assad.
Rayeq said he wished the presidential nomination had been made "in a more democratic, participatory way".
Authorities have pledged to hold a national dialogue conference involving all Syrians, but have yet to set a date.
"We thought that the national conference would see the creation of (new) authorities and allow the election of a president -- perhaps Sharaa, or someone else," Rayeq said.
"But if we are realistic and pragmatic, (appointing Sharaa) was perhaps the only way forward," said Rayeq, who since Assad's fall has helped found an initiative on human rights and political participation.
- 'Consolidate' -
Authorities have suspended the constitution and dissolved parliament, while the army and security services collapsed after decades of Baath party rule.
Ziad Majed, a Syria expert and author on the Assad family's rule, said Sharaa's appointment "could have been negotiated differently".
"It's as if the heads" of the different armed groups chose Sharaa, Majed said, while noting the leader was effectively "already acting as a transitional president".
Sharaa said his appointment followed "intense consultations" with legal advisers, promising a "constitutional declaration" and a "limited legislative council".
Majed said most armed groups "recognise Sharaa's leadership", but noted unresolved tensions with fighters in the south and northeast.
Armed groups in the southern province of Sweida, including from the Druze minority, have been cautious about the new authorities, though two groups said last month they were ready to join a national army.
In the north and northeast, the Kurdish-led Syrian Democratic Forces from a semi-autonomous Kurdish administration have been battling pro-Turkey fighters.
Syria's new rulers, also backed by Ankara, have urged the SDF to hand over its weapons, rejecting any Kurdish self-rule.
Majed said he expected "Sharaa and those close to him" to seek to "consolidate territorial control and control over armed groups", but that other priorities would include reviving the war-battered economy.
He also cited sectarian challenges and the need for efforts to avoid "acts of revenge", particularly against members of the Alawite community, from which the Assads hail.
- 'Too early' -
Lawyer Rayeq said he supported grouping Syria's ideologically diverse armed groups "under a single authority, whatever it is".
If such a move were successful, "we will have put the civil war behind us", he said.
Assad's toppling has finally allowed Syrians to speak without fear, after years of repression, but concerns remain.
Dozens of Syrian writers, artists and academics have signed a petition urging "the restoration of fundamental public freedoms, foremost among them the freedoms of assembly, protest, expression and belief".
The petition also called for the right to form independent political parties and said the state must not "interfere in people's customs", amid fears Islamic law could be imposed.
Spare car parts seller Majd, 35, said the authorities' recent announcements were "positive", but expressed concern about the economy.
"Prices have gone down, but people don't have money," he told AFP from a Damascus park with his family, noting hundreds of thousands of civil servants had been suspended from work since Assad's overthrow.
Near the capital's famous Ummayad square, vendors were selling Syrian flags, some bearing Sharaa's image.
"It's too early to judge the new leadership," Majd said, giving only his first name.
He said he preferred to wait to see the "results on the ground".
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