Ask Electronics

As a young child, I had a wooden board with a bunch of different light switches mounted to it. Nothing to tinker with, but I had a lot of fun with the physical sensation of switching them on and off. I think that's all you can really ask for at that age.

Later on, I enjoyed taking the switches apart, figuring out how they work and using them in my electronics projects.

My point is, whatever you choose should be physically fun, even without understanding it. A few switches and maybe a blinking light can entertain a toddler for a long time. The tinkering can come later.

Growing up I usually had a little 50 in one or 100 in one electronics project kit.

Keeps all the stuff on one kit, and you connect wires under little springs. Still adult supervision required for sure, but on the upper range of what's possible.

Breadboard is a cool idea, but your first experiments will likely be super simple right?

Here’s a few thoughts.

How about some double conducting copper tape and sheets of craft paper or cardboard. (Double conducting conducts on the top as well as the sticky side so overlapping joins completes the circuit).

You can draw/plan and then route the copper sticky tape like a circuit board. Fashion basic switches from the copper tape around a cardboard flap, tape down any “flat” components like resistors.

Add some tinned leads to anything that would stick up from the board.

I often find the more tactile “MacGyver” approach is a better teaching aid as there’s no mystery behind the scenes (no hidden board wires, no pre-mounted components or connectors). Everything is built up from existing skills and experiences.

When you start to get more advanced, 80s Aussie kids grew up with:

https://archive.org/details/dicksmithsfunwayintoelectronicsvolume2/Dick%20Smith%27s%20Funway%20into%20Electronics%20Volume%201/page/n5/mode/1up?view=theater

That has a complete list of components needed for the projects in the book. Same idea as the copper tape, just with bits of wire and screws. The project in the book were all built onto a pre-drilled block of plastic with the schematic laid on top. They were fun little projects and easy enough to do - the flashers and sirens were a hit for me.

maybe something like littlebits kit? I haven't tried them myself, but they look fun, educational and kids friendly (not sure about 3yo thou)
https://www.youtube.com/watch?v=E7B0mWvnE1Q

Play memory or with a wooden kitchen. I'd say 3 is too young. you can get some basic electronics kits for children. just visit one of the toy stores. But playing with electronics and doing experiments starts being fun at around 5 to 8 years. Maybe playing with an extension cord at 4. but you wouldn't want to encourage a little kid to play with extension cords, plugs and mains power...

I loved electronic snap circuits when I was 5-8 or so, so that's definitely a good one if they still make them

Get them working on their mathematic skills, instead. You can give them a really good head start - mine could solve simple differential equations at age 11.