Hey, working in DevOps, went from working in a small 110 people company to 12,000. You will be fine. Actually you might be better than most of them.
What I have discovered is that in small companies you wear many hats. Maybe you do DevOps, but you probably also control database administration, maybe you owned physical servers so you have experience working with racks. In a small company you are pretty much IT, you might even reset passwords, setup networks etc.
In bigger companies everything is controlled. There is a VM team, that doesn't have access to the OS, it's a different team. The networking team is split, they might even have different managers or executives controlling them. It's actually my biggest frustration, working in a PoC and not being able to access some logs in a machine because I don't have access to it.
Also I find that a lot of times, no one knows the answers to obvious questions because the larger the company the less visibility you have on who is doing what.
At the same time, occasionally it's nice to be able to say, I don't have admin access to this, ping XYZ team. The pay is noticeably better as well.
So, treat it like any new job. Take notes, learn how things works, ignore politics for a while, figure out who the mover and shakers are and go from there.
You'll be fine. Also remember this, companies develop their own vocabulary over time. So don't be afraid of asking what they mean by something. Even if you think it might be basic, and if you get the look of WTF, just be honest and say look I get companies have different vocabs, I just want to make sure I am 100% on the same page. 99% of the time if you use your honeymoon period well and do this you can easily learn the ropes, and figure out how to fit in and stand out. If you try to be a hero or think oh I have to know this even if you have no clue what they mean, that's when I see people fail.
I saw this at one mid-sized company where they had weird verbiage for things that I thought were standard. New people would always struggle and two people even left over it cause they were making it into something it wasn't and would get themselves stressed out and tied into knots instead of just asking the question. I was a consultant there and some of the employees would look at me like I was dumb at first, but the reality is I had to learn their terms, process etc before I could really help them.
Thirty years ago I went from self-taught programmer to working for a 10,000 ppl company almost overnight. Turned out to be a great thing, and I bet you will do great also. My one pithy bit of advice for Big Company work: try to stand out, and fit in, at the same time.
The question we all ask ourselves:
Do I suffer from Dunning -Kruger, or Impostor Syndrome?
Relax, learn the ropes, find where you can add value. And learn.
Hey you made it. Congrats!
Do not worry, they would not hire you if you were not good fit. And if they are top in the market they definitely have mentoring and multiple paths for you, already ready. Yes it might be hard at the beginning, give your 100%, maybe 110% ;) and you'll do great and learn a lot on the way.
Cheers