I've thought about this, and have done a playthrough of New Vegas as the Lone Wanderer.
How do, you ask?
Ron Pearlman Voice: "An expedition had been planned to reconnect with the Western chapters of the Brotherhood, a decision to make up for bad blood. What the Lone Wanderer and his team didn't expect was to have the old Veribird they'd taken from the Enclave shot down over California territory. NCR. Brotherhood. Super Mutants. Or maybe just a raider who wanted to try out the rocket launcher he'd dug up. Either way...Cut off from the East, and no allies, the team parted ways to make the best of it. The Lone Wanderer, ever the one to put his nose in other peoples business, wound up a Courier for the Mojave Express. Good work, simple work, and plenty of opportunity for trouble...Then that damn chip happened."
If I wanted to make it work for Falloout 4, all I had to do was look to the Think Tank in the Big Empty and their cracked out science.
RP Voice: "Time Travel. For the Think Tank it was all theoretical. But it was always something they'd come back to every so often, more so out of boredom and in between experiments. And lucky for them, they had a live-in ready test subject who was always more than a little eager to throw themselves in for the good of science. All they wanted was data on the Old World, things long forgotten. He was only to observe, and never get involved, but the Lone Wanderer...just can't help himself. It was bad enough the Recall device short circuited when he woke up naked in a parking lot, leaving him effectively stranded in the Back When. I guess the Think Tank didn't consider everything. He was stuck again in a strange alien world, completely different from the one he left behind.
"It wasn't all bad...He'd found love in this world, and a family. He could put the old ways behind him. Be happy. Live simply. Enjoy food that wasn't prepackaged garbage. Ah...But he forgot the most important rule. War. War never changes...And the past is damned to repeat itself."
Lone Wanderer 111: Emerges from the vault. "DAMMIT!...Oh well...Good be home..."