A couple of times, according to Paul, those treks involved a visit to an emergency room on the tournament grounds: his sister was once bitten by a poisonous spider and then his mother passed out and hit her head after seeing a player get badly injured.
"Every year we always had something terrible happen," said Paul.
This trip to Flushing Meadows is going far more smoothly though for the No.14 seed.
The 26-year-old earned a debut appearance in the fourth round at the Open by hitting 15 aces and getting broken just once during a 6-1 6-0 3-6 6-3 win over No.21 Alejandro Davidovich Fokina of Spain in Arthur Ashe Stadium on Friday.
"I was kind of, like, 'really, they're putting me on Ashe?' I knew there was a pretty strong schedule of people," said Paul, who never before had played in the 23,000-seat main stadium.
"I was kind of surprised. ... Hopefully I'll be back many more times."
At least one American is now guaranteed a spot in the quarter-finals, because Paul's next opponent is unseeded Ben Shelton, a 20-year-old from Florida.
Shelton advanced Friday by defeating Aslan Karatsev of Russia 6-4 3-6 6-2 6-0 with the help of 26 aces.
Also into the fourth round is No.10 Frances Tiafoe, who was a 4-6 6-2 6-3 7-6 (8-6) winner against No.22 Adrian Mannarino of France.
The 25-year-old Tiafoe reached his first grand slam semi at the US Open a year ago - beating Rafael Nadal before losing to eventual champion Carlos Alcaraz - and is the first man from the United States to get to the fourth round in New York for four consecutive years since Andre Agassi in 2002-05.
Tiafoe was not exactly in fine form ahead of his return - he lost three of four matches on hard courts leading into this Open.
Not that he cares about that now.
"The summer's irrelevant," Tiafoe said. "It's all about this tournament, honestly."
Entering the 2022 US Open, Paul never had won a match at the place. Then he claimed a pair of five-setters before bowing out in the third round against runner-up Casper Ruud.
"Normally when I'm done with tournaments, I don't watch anymore," said Paul, who signed his initials on one fan's head Friday.
"But 'Foe' is pretty much my favourite player to turn on and watch, so I couldn't not tune in and watch it."
Joining Paul in the round of 16 is Australian wildcard Rinky Hijikata, who fought off a fightback from Chinese trailblazer Zhizhen Zhang to post a 6-3 6-3 4-6 6-3 win.
Dominic Stricker also went through by beating Frenchman Benjamin Bonzi 2-6 7-5 7-6 (7-4) 3-6 6-2.
The Swiss will now meet No.9 seed Taylor Fritz, who toppled Jakub Mensik 6-1 6-2 6-0.
