You can still be an engineer if you don't memorise all those configurations, and the most important formulae, but you won't be a very good one.
There's always Google, but if you have to look stuff up every time you see a transistor or need to design something with one, then it will take you forever to actually complete anything.
If you don't have a library of common solutions to common problems already in your head, how can you possibly know what approaches exist to solve a particular problem?
I don't think the formulae are as important as the conceptual understanding, but still, you must at least know by heart the basic transistor configurations and some of their variants.
This isn't as difficult as you think. All this comes from experience, and you don't necessarily have to study from dry, boring books. Actually make these things. Try to understand real life circuits. You'll store all this information quite automatically, without having to memorise by repeating some meaningless phrase in your head, over and over, like you do with multiplication tables.
Every time you actually apply some concept, you automatically learn it, and store that knowledge for later. At the very least you'll remember that you did "something like this some time ago" and have an inkling of where to start. You can always look something up, but you have to know what to look up in the first place.
Just apply what you learn. Do exercises, make circuits. Actually use the information, rather than just try to remember it.