Cpl Bryant was serving in the Intelligence Corps
A special forces staff sergeant has told an inquest there was "disbelief" when his troops found out they would be using Snatch Land Rovers on patrol.
He was in charge of Cpl Sarah Bryant and three SAS reservists - Cpl Sean Reeve, L/Cpl Richard Larkin and Pte Paul Stout, who died on patrol in 2008.
The staff sergeant, known only as "O", also said they had no training with bomb detectors before deployment.
Cpl Bryant is the only British female soldier to have died in Afghanistan.
Coroner David Masters said the six-day inquest would look at the soldiers' equipment, training and mine detection drills.
The four were in a Snatch Land Rover, a light vehicle in which at least 37 UK soldiers have died in Iraq and Afghanistan.
The lightly-armoured vehicles' vulnerability to roadside bombs and other explosives has led some soldiers to call them the "mobile coffin".
Wiltshire and Swindon Coroner David Masters said the inquest would look into the suitability of Snatch Land Rovers for such patrols, the type of metal detectors used and the drills carried out for landmines and roadside bombs.
Mr Masters told the inquest: "The bounds of this inquest should encompass issues relating to the concerns about the suitability of Snatch Land Rovers by reference to their capability and another concern which was expressed about [their] training."
He added: "Another issue that we considered at the pre-inquest hearing relating to the death of L/Cpl Larkin is whether or not a collapsible steering wheel could be fitted."
Post-mortem examinations showed that L/Cpl Larkin had died of blunt injuries to the chest and abdomen following an explosion.
The others died of blast wounds caused by an explosion.
The back wheels of their Land Rover hit a 50kg to 100kg (110lb-220lb) pressure-plated improvised explosive device (IED), or roadside bomb, as they crossed a ditch.
Mr Masters said: "Its rear wheels detonated a massive explosion, causing immediate devastation to the vehicle and in probability the instant deaths of Cpl Bryant, Pte Stout, Cpl Reeve.
"L/Cpl Larkin, the driver, was trapped by the steering wheel in the upturned vehicle and was also found to have died."
'Criminal at worst'
The Snatch is agile but lightly protected and was never designed to take the full force of the blast that killed Cpl Bryant and the other three soldiers, says the BBC's Jonathan Beale.
The deaths, in particular that of Sarah Bryant - a young, recently married member of the Intelligence Corps - attracted a lot of media attention at the time.
The incident also attracted a lot of criticism, with one SAS major resigning his commission in protest.
Maj Sebastian Morley told the Daily Telegraph at the time that the Ministry of Defence's failure to provide troops with adequate equipment was "cavalier at best, criminal at worst".
Concerns about the vehicle were raised as long ago as 2003.
The MoD has upgraded the Snatch with improvements to its armour and better electronic counter-measures to detect makeshift roadside bombs. But that work has yet to be completed.
This January, the Army started to receive the improved Snatch Vixen Plus but the older models are still in service in Afghanistan.
In a statement, the MoD said its thoughts were with the families of Cpl Bryant, L/Cpl Reeve, L/Cpl Larkin and Pte Stout but it would not comment on ongoing inquest proceedings.
It added: "We have made clear many times that the safety of our personnel is our top priority and the MoD has spent over £1.3bn since 2006 on new and upgraded vehicles.
"The threat our forces face in Afghanistan has continued to change and we have evolved our protected vehicles to match the threat. Snatch Land Rovers are no longer used in areas of heightened threat from IEDs."