The American was announced as team-mate to Alex Albon for 2023, contingent on him securing the requisite licence points.
Williams promptly confirmed the 21-year-old, this time without the caveat, as its second driver in 2023.
“The pressure was high but I think the benefit was knowing early what the situation was,” Sargeant said.
“It gave me time to come to terms with it and appreciate what was on the line.”
With his licence secured on Sunday, the American was in action for his new team on Tuesday as part of the post-season test.
That saw him clock up 82 laps across the day in what was his first opportunity to let off the shackles in the 2022 car.
During his previous outings, designed to secure a bonus Super Licence point in case it proved necessary, his focus was on staying out of trouble and completing 100 km of running.
“The FP1s gave me a taste,” Srgateant said of his recent Friday outings at F1 race weekends.
“I don't think they fully allowed me to get comfortable in the car because I never really completely pushed because I needed to get those extra Super License points just in case.
“Obviously it gave me a taste of speed, the brakes, the downforce, but [the test] was the first chance I really used started to use all of it
“The most important goal [in the test] was to, one, get comfortable in the car and really push the limit,” he added.
“In the FP ones, you know, it's touch and go because you need to get your 100 k's, and you don't have much time.
“[In testing] I could really find the limit and get comfortable with it, as well as just really learning how I can change the car balance to my suiting just through the steering wheel.”
The variety of controls available to him in the car proved the steepest learning curve.
Part of his programme involved the team instructing him to make switch changes while out on track.
“There's a lot going on,” he admitted.
“They were definitely testing me, making me do a lot of switch changes just to make me think about more than one thing and try and get me used to that, which is difficult.
“But there's no better way to pick up on that [than] by doing it.”