I've used this analogy before but it's a good one; a cousin to the bucket and the leaky faucet.
Imagine water flowing into the top of a large tank. The water is solar energy and the tank is the Earth's energy content. Near the bottom of the tank, we have a drain line with an adjustable valve that lets the water back out. In the Beginning (da-da-da-dummmmmm), the tank was empty and the water started pouring in. When the water is shallow, there is very little water pressure down at that drain line and so not much flow. The water keeps rising because its coming in faster than its going out. But as the water gets deeper, the flow out the drain line increases. At a certain depth, that increasing depth will have gotten the flow out of the drain to equal the flow in. The water depth will stop changing and everything is stable. The system is at equilibrium.
Now, we change something. We could increase the rate that water is flowing in. That would cause the water level in the tank to rise till the increasing pressure had pushed the outflow to match. We'd have a new equilibrium at a new water depth. If we decreased the flow in, the reverse would happen and we would establish a new equilibrium at a lower water level. Alternatively, we could adjust that drain valve. If we open it up, the outflow will exceed the inflow and the water level will drop. If we close it down a bit, the opposite will happen and the new equilibrium will be at a higher water level. Or we could do both. Increase the inflow and increase the outflow. If you're careful, you might keep the equilibrium right where it was at. Or you could make the adjustments in opposite directions, making the water level change even faster.
This is why adding CO2 to the Earth's atmosphere, even in small amounts, has a significant effect over the time scales under consideration here. We could close that valve just a tiny, tiny, tiny bit and it would look as if nothing was happening. But it has and that water level will rise and it will keep rising till it finds that new equilibrium. CO2 resists the escape of thermal energy from the Earth. It closes down that drain valve and raises the level at which the system will reattain equilibrium. And CO2 has a long lifespan in the atmosphere: hundreds of years. Almost every bit of CO2 that humans have added to our air is still there. And keep in mind that when you want to look at a percentage change in temperature with regard to physical and chemical effects that will cause, you have to do that on one of the absolute scales. It is not correct, if yesterday was 70F and today it's 80, to say that it is (10/70)% warmer, because the zero on the Fahrenheit and Centigrade scales are arbitrary. Zero temperature is absolute zero and thus, so far, global warming has only produced a change from 286.9 Kelvin to 288 Kelvin. That's enough to be seen and to have effects and, since we are closing that valve faster and faster, further and further every day, the rate of water level change, the rate of temperature change is still accelerating.