Caoimhe O’Brien was killed in a crash on the road between Derry and Strabane in October 2016.
Her mother Marie said the long-awaited work “would save a lot of lives”.
Her comment came as Mr O’Dowd held a virtual meeting with Derry City and Strabane District Council to give an update on the dual carriageway project.
Mr O’Dowd told the meeting he was determined to do everything he could to progress the road scheme.
He said some of the major delays were down to groups or individuals taking legal challenges.
“Every time there is a legal action against the A5, you can add a year to 18 months to the clock for the completion or the start or the A5,” he said.
The work, which is estimated to cost about £1.2bn, would connect Derry to the border at Aughnacloy and improve access to Dublin.
It was first announced in 2007 but the A5 Western Transport Corridor (WTC) scheme has been beset by funding issues and legal challenges.
The flagship scheme featured in the New Decade, New Approach deal, which restored power-sharing to the Northern Ireland Executive in 2020 after three years of deadlock.
The scheme is the single largest road scheme ever undertaken in Northern Ireland.
Mrs O’Brien, who will be requesting a meeting with the minister, said there were still so many questions about the night her daughter died.
“There were things that were never explained to us and we don’t really know what happened,” she told BBC Radio Foyle.
“We think the car went out of control at 45 miles per hour and unfortunately it hit a wall and Caoimhe didn’t survive.
“That night destroyed our lives, it devastated us and we have never been the same since.
“The house is empty without her… that knock on the door will live with us until we die.”
Mrs O’Brien said a lot of lives would be saved if the work started sooner rather than later.
“Every week you hear of accidents on the A5 – not all of them are fatalities but there is a lot of fatalities,” she said.
“Every time I hear of one my heart just goes because I know another family has to go through what I went through.”
Speaking at the council meeting on Wednesday, the infrastructure minister said the A5 was “simply not fit for purpose”.
“Since 2011 there have been 32 lives lost on the A5, and there have been five lives lost in recent months,” said Mr O’Dowd.
“Each one of those is a story in itself, it is not a statistic, and family homes across our island are missing loved ones as result of accidents on the A5.
“While all roads carry certain dangers, it’s quite clear the A5 has now become a road which is presenting dangers to its users because of the volume and the type of road that it is.“It’s simply not fit for purpose and hence the reason why I am so keen to progress the A5 for road safety reasons and economic development reasons.”
Mr O’Dowd said his department was due to meet the Planning Appeals Commission (PAC) in early spring to present their response following a public consultation.
He said if the PAC’s findings were positive, then construction work could start as early as 2024, with a potential completion date of 2028.
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