How do I bake cakes in a gas oven without a temperature knob?

I'm afraid you're going to have to use a thermometer if you want to have any reliability. Hopefully your oven holds a reasonably steady temperature so you'll be able to match what recipes call for. Oven thermometers are really cheap; if you tried to do without it you'll probably waste more money on ingredients for failed cakes (not to mention the time) than you would have spent on the thermometer in the first place.

The thermometer will end up telling you how long it takes to preheat as well; once you see the temperature stabilizing you'll know it's preheated enough. The actual amount of time will vary a lot; it could be 5 minutes for a powerful oven aiming for a low temperature, or 20 minutes for a less powerful oven aiming for a high temperature.

I agree with Jefromi that the easiest solution is just to get a cheap oven thermometer that you can put into the oven. I'm not sure where you're from or the availability of them, but they are generally quite cheap.

Before such things existed, people had methods for testing oven temperatures for baking. The most common one was to put your hand into the oven and count how long it takes until it's too hot and you need to take it out. Depending on the number of seconds, you could tell the difference between a "hot" or "moderate" or "low" oven or whatever. Such distinctions are sufficient to determine oven temperature to bake a passable cake, but they require experience to achieve even basic precision. If you already knew how to do this, you could estimate the oven settings pretty quickly (though only in a general sense, but good enough for basic baking).

But without that sort of previous experience, I'd again just recommend buying an oven thermometer.