Jack Hurn and his girlfriend Alex Jones received the first doses of the vaccine on May 29, 2021.
When the couple arrived at Dudley vaccine centre, lawyers say they were allegedly told there were no Pfizer vaccines available.
The pair then allegedly asked staff about alternative vaccines as they were "aware of concerns around the use of AstraZeneca for younger people".
Medical advice at the time recommended that under-40s should get an alternative to the AstraZeneca vaccine after it was revealed that younger people were at greater risk of blood clots.
The family's lawyers say staff were said to have reassured the young couple that the AstraZeneca vaccination was safe, and they went ahead with it.
Days later, Mr Hurn started to suffer from headaches.
He was then taken to Birmingham's Queen Elizabeth Hospital where doctors allegedly described him as having "catastrophic" blood clots on the brain.
Mr Hurn died on June 11, 2021.
His family are now hoping that an inquest which started on Monday (23 May) at Birmingham and Solihull Coroner's Court will answer some of the questions they have around Jack's death.
Lawyer Michael Portman-Hann, said: "Jack, a first class honours graduate of Coventry University, had recently bought his first home with his partner, Alex Jones, who also received her vaccine at the same time.
"She only found out after his death that he was planning to propose that summer.
"Jack’s parents, Tracey and Peter, his sister, Abby, Alex and both their families are completely devastated and are still trying to come to terms with what happened.
"Jack and Alex asked staff at the vaccine clinic about the Pfizer alternative as they were aware of concerns around the use of AstraZeneca for younger people.
"Alex and Jack were reassured by the staff at the centre that the vaccine was safe, and with no Pfizer doses available that day, they felt encouraged by vaccine staff to go ahead with what was on offer."
Mr Portman-Hann continued: "Jack began to suffer headaches which got progressively worse and he was admitted to the Alexandra Hospital in Redditch where a scan revealed a clot on his brain.
Jack’s family, who live in Devon, found it very difficult to get up-to-date information from hospital staff over the course of a number of days.
He added: "They say there was confusion about whether Jack had actually suffered a stroke while at Redditch and could get no clear answers about his condition.
"Given the family’s concerns over advice given during the vaccine clinic visit and what happened in the period between Jack being admitted to hospital and his death, we are supporting them to find answers which we’re hopeful an inquest will help provide."
ITV News Central has contacted NHS England for a response. However they have said they will not be commenting while the inquest is ongoing.
You can find informed, accurate information about the coronavirus vaccine on the NHS website - including who is currently eligible to receive it, how it is administered and information on the safety and side effects of the vaccine.
Oxford University also runs the vaccine knowledge project which offers reliable and authoritative information on Covid-19 vaccines. This page includes facts on how the vaccine was developed, the outcomes of the trials for different vaccines and an explanation of the technology used by each vaccine in simple terms.