On the eve of his birth, the Southeast African republic's first democratically elected Hutu president, Melchior Ndadaye, was assassinated by Tutsi soldiers during a failed military coup.
Within a year, the ensuing conflict would have claimed an estimated 100,000 lives. By the time it was deemed to have ended in April 2005, almost 300,000 people, mostly civilians, had perished.
To say that Bigirimana has been on his own particular odyssey since his father, Bonnet, spirited him and his three siblings to safety in Uganda several years into the bloodshed is an understatement.
It has now led him to the front doors of Rangers, a place in which they have the effrontery to call a few years of attempting to scramble through Scottish football's lower leagues 'a journey'.
The 21-year-old spent four years separated from his mother, Esperance, who left to carve out a new life in England. He was 10 when they were finally reunited in her new home town of Coventry, where Bigirimana would take his first steps towards a career in professional football after turning up unannounced at the Coventry City academy and demanding to be given a game.
A transfer to Newcastle United in 2012, for a fee reported to have been as much as £1m, has brought its own frustrations since he fell out of the first-team reckoning, but this is a young man accustomed to hardship and unfazed by it.
Coming to Rangers on loan is, he says, "a gift from God" and the perspective that comes from such humble and precarious beginnings gives him a real sense of positivity about the challenge he now faces in trying to win round a cynical support and help his new club peg back Hearts' substantial lead at the top of the SPFL Championship.
"I look at my life as a miracle," he said. "Everything I go through, I am learning. It is a journey for me as a footballer and I love challenges.
"In the last two years, I haven't been involved at Newcastle and it has been tough, but it has made me learn. This is a reward for my patience, so I can't wait
"The few players around the world that make it are the ones that have strong character. When you are going through a tough time, that doesn't mean you are not good enough.
"It just means that something around your life is working for your own good.
"This is an opportunity for each one of us to show what we can do, not just to Rangers fans, but to the world. The biggest target is to get this club back where it belongs and to be successful because that is why this club is known.
"Yes, we are 16 points behind Hearts, but we have got two games in hand.
"We are here to go up. We are still young in football, but this is an opportunity for us to grow as footballers and men."
Bigirimana's life has certainly brought obstacles that no doubt caused him to grow up rather more quickly than he might have liked. He remembers little of his family's decision to flee Burundi, but has spoken at length in the past about the difficulties of being estranged from a parent at such a young age.
"We had to get out of Burundi when the civil war began," he said "We had to get to a country that was safe and, at first, that was Uganda for us. For my mother, it was England.
"My mum left first and her sister brought her to England when I was six or seven.
"My dad was a town planner, my mum braided hair, my brother worked in a shop. Even when I was little, I would run errands for the local shop. By Burundi standards, we were doing well.
"We got separated from my mum for four years, but she rang us and she said: 'I'm in England and my plan is to bring you guys here.'
"My mum took a huge step of faith to leave us, but there was nothing that would stop her from making life better for me, my sister, my two brothers and my dad."
As if Bigirimana's story is not remarkable enough, it was while heading to Asda to buy some milk on his mother's insistence that he showed his ability to grasp an opportunity with both hands and, aged just 10, opened the door to a football career.
"I was walking past the academy, near our house, with my brother and I heard a whisper in my heart that told me to train with them," recalled the deeply-religious midfielder. "I know it sounds crazy, but I knew the whisper was God and I said that it was down to him to make it happen.
"I managed to get into the training ground. I went to the reception, but my English wasn't very good, so they sent me to the scouts, Ray Gooding and Reece Brown.
"They told me they would come and watch me play at my school if I sent them a letter.
"As I was jogging up the hill to go back home, they stopped me. They called me back and said: 'Do you have your own equipment? Boots and stuff?'
"I didn't, but I said yes and then they said: 'Come back tomorrow and start training.'
"They explained to me later that they saw athletic speed, but I was not really running. I went on trial and they signed me."
Bigirimana insists he understands the turmoil enveloping Ibrox at the moment. He realises the club is at its lowest ebb, but negativity simply does not seem to feature in his vocabulary.
"People might say we don't know what we have let ourselves in for, but you have got to have a target," he said. "You can't live your life in fear thinking: 'I don't think it can happen'. Anything can happen."