My objective has often been to build & test as many experimental circuits as I could in the shortest amount of time.

One of the real good shortcuts is to just start soldering parts together according to a plan in your head, without taking the time to make a schematic drawing beforehand or do any advanced calculations.

There might be more emphasis on the properties and ratings of each component this way, this is not something to skip over, you should be very familiar with each component you use. Well in advance, and loads of hours of component study needs to be behind you, otherwise you may not do too good at just whipping something up on the bench that's electrically sound to begin with.

As pointed out, with math it can be the same way.

If you just want to quickly start picking up parts and soldering them together right away without doing any advanced calculations, the best shortcut is to have already become quite familiar with the equations including calculus when necessary, so you can bring to bear endless hours of mathematical study and use it to intuitively guide your soldering iron for every hour at the bench.

Edit: upvoted because your message should not be less than neutral, not greyed out at all. Obviously, I'm on the fence, sometimes I use math, other times not at all ;)