It's possible if you keep things simple, but it's a rather naive goal in most places which have already grown in size and complexity. Just knowing what's happening with the other teams and how your work fits into it is already a full-time job. I've spent DAYS on Slack without getting anything done - I had to get up early in the morning.
Read books, on a variety of topics, including the ones you don’t know about. A book will give you a much broader and deeper understanding of most topics than random blog posts on the internet. Make sure you read one or two a year, and think about how you’d apply what you’re learning at work. Even better, find an actual application at work.
I’ve found that solving tricky problems ( horrible network related issue, performance bugs, strange behaviour of program/framework/os, someone you know deciding to use new tech you don’t know about etc ) is usually a good way of finding a topic to explore.
Find someone who’s interested in actively learning things, it makes things a lot more pleasant, and it’s easier to remain motivated. You don’t have to learn the same things - just share the fun stuff you’re learning.
Finally, and most importantly : it’s ok if you’re not learning as quickly as when you were at university. It’s not a competition. You have a full time job, don’t have a lot of time, so just make sure that you enjoy learning, so that you keep doing it !
Don’t stop learning at the end of your use-case for a piece of tech. If your team uses a tool, understand approaches you didn’t take, trade offs and ultimately why you chose the path you chose. Understand even other pieces of tech and their approaches. Also, deeply understand failure scenarios and how to mitigate them.
Basically just dig in beyond “it works”. You’d be surprised how many devs never read a tool’s docs if they don’t absolutely have to.
In general, how would someone go about this? Is it just something that should happen over time or is there a method/goal to strive for?