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.