The United States international made his move to Chelsea official last summer, after they agreed a £57.6 million deal with Borussia Dortmund in January 2019 before loaning him back for the rest of the 2018-19 campaign.
Pulisic's first season in the Premier League has been disrupted by injury, with six goals in 23 appearances before the coronavirus pandemic halted sport across the world.
He told Jermaine Jones on the 13&ME podcast of his experiences at Chelsea: "It was all pretty crazy what happened. I had to fly straight from my summer break right after the Gold Cup. I had one week off and I didn't really get a summer.
"The team had already started preseason in Japan so I flew straight there and I had to literally fly by myself and then meet the team who had flown from London.
"I had to go straight to the hotel and the next thing on the schedule was to go straight to training. I was tired, nervous and didn't know what to think but: 'I'm at Chelsea and this is insane.'
"I got on the bus, they had just arrived as well. Everyone is half asleep, I go and sit on the bus and nobody even noticed me. Nobody said anything. There were maybe one or two guys who said: 'Hey, hello' and I was like: 'What's going on here?'
"Those first couple of days of training I was nervous. You know how it's like when you move to a new team."
The 21-year-old, who features in ESPN's list of the best players aged 21 or under, said he needed to win over his new teammates following his move from the Bundesliga.
"They're nice guys off the field but to earn that respect you have to show on the field you have that ability, that's just how it is," he added.
"I had to go in on day three when I had a really good training, scored some goals, had some nice plays and assists and then I felt the guys coming and talking to me and getting their respect.
"It's interesting how it works but they've been great guys and I've enjoyed it."