Bearman was called in after Sainz was ruled out of the rest of the Jeddah event due to appendicitis, with the Spaniard requiring surgery.
The 18-year-old had to abandon his Prema F2 seat, having secured pole position for Saturday's feature race, and had only FP3 in which to find his feet before heading into qualifying.
He made a strong impression with a confident performance that saw him just miss out on Q3 in 11th place.
Revealing the advice given to him by Ferrari team principal Fred Vasseur, Bearman said: “Fred, he doesn't say much, but what he says, he means. He was very clear to me that I have to build it up, step-by-step. Don't try to be a hero.
“Especially after FP3, which was already a good session, his goal for me was just to keep going like that, and build it up step-by-step.”
Although Sainz had felt unwell on Wednesday and Thursday, Bearman insisted that he had no idea that he might be required.
“Honestly, no,” he said when asked by Motorsport.com if he’d been put on standby. “I woke up this morning fully prepared and fully ready for my [reverse grid sprint] F2 race, starting from P10.
“I got the call pretty late on in the day, just a couple hours before FP3, that I will be doing it.
“Of course not the circumstances I would like to make my F1 debut, and I wish the best to Carlos and hope he recovers well. But nonetheless, it's a fantastic opportunity.”
Bearman's F1 debut carries with it some notable statistics, with him being the first driver to make their championship debut with Ferrari since Arturo Merzario in 1972 and the youngest British driver ever to compete for the Scuderia.
“The stars have aligned," he said. "It's been such a quick progression in my career.
“Two years ago, three years ago, I was in F4 still, I only did my first F1 test like three or four months ago.
“So it's been a really quick progression. And yeah, to make my F1 debut in red, hopefully a sign of things to come.”
Bearman said the lack of warning worked in his favour, as he didn’t have time to appreciate the magnitude of the situation.
“I honestly didn't have time to get nervous or to overthink it,” he said. “Because it was so late that I literally had to focus straightaway on trying to get up to speed, and catch up the lost time.
“Having missed out on Thursday made my life a little bit more difficult, let's say. So I was pretty much flat out with the engineers trying to figure out everything and get up to speed as quickly as possible.
“I didn't have time to think about the gravity of the situation. Maybe that was a good thing.”
He admitted to some frustration at not nailing his first lap at the end of Q2 and thus not progressing to the final session.
“I think the main loss was that I did the lap on lap two,” he noted. “My first lap was a bit scruffy in sector three, and I lost a lot of time there. And yeah, the tyres aren't in the best window for lap two. So that's my mistake.
“And I felt like my lap two was pretty decent. You know, the gaps are so close, I see little pinches of time here and there, but that's how it is. It's fine margins.”
Asked if he was planning to take a patient approach to the race, he said: “Exactly. That's my goal. No mistakes and build it up. Get to the end, avoid any carnage, and build up some experience in myself. And hopefully, bring back some points at the end.
“It's a big step from F2 in terms of physicality. But I always feel prepared to make my debut - that's what I've been training for, in case this F1 opportunity comes up, and it finally has. So hopefully I can make it stick and do a good job."
Bearman has no concerns about compromising his F2 title campaign by missing the two Jeddah races.
“I mean the thing is the goal of F2 is to get to F1,” he noted. “So I get this opportunity, there's no way I'm going to let it go. I think if I have a good weekend here in F1, it shows a lot more than winning the feature race and doing pole in F2.
“I did half the job in F2. I did pole. And hopefully, I can bring back some points, and show what I'm capable of.”