The thing you are missing, which is a massive hurdle that is underappreciated, is that you need access to raw materials. Most of the modern gadgets we use require things that you can't just find out your front door.
That's why it takes a hundred years. You first have to create the infrastructure that allows you to free up people to prospect and mine. However if we concentrate on energy first then most of the materials one needs to get started are indeed just outside one's front door. All you need for an electronics industry is glass and metal. We can use valves until we have a supply of indium, etc.
