How can I bake muffins without an oven?

This is pure conjecture, as I've not actually tried doing this.

Muffins are quickbreads, and as such, are fairly similar to cake.

And there are a lot of recipes out there where people make cupcakes n a mug then microwave it.

Serious Eat's directions for microwaving a cake in a mug are:

Wipe inside rim of cup to remove excess batter. Microwave on High power until cake has risen and looks moist (not wet) on top, checking every 30 seconds, about 1 to 2 minutes. Avoid overcooking or it will be dry. Let rest to cool briefly before topping with ice cream and eating.

... but the time is also going to be dependent on the amount that you put into each cup, and the dimensions of the mug (tall & slender vs. short & wide), but I would make them one a time and experiment with the time as you use up your batter.

You can actually steam a lot of cakes. The basic idea is seal the cake pan tightly with foil (or even plastic wrap if your can handle the temperature) and then place it in your steamer insert/basket. I find it takes about 40 min for it to cook all the way through. Makes for a super moist and fluffy cake. Here’s a random example I found online. Paper in reference to streaming gluten free cakes (which is where I first got the idea)

If you have an option of 'convection' in microwave settings then you can adjust the temperature (in °C or °F) and hence use that as oven. Also cakes/muffins can be made in the same way, in microwave but then in microwave proof vessels. For that you may take a microwave proof container say a square plate, grease it and pour the batter. The plate should have a height or else, the batter will come out. Now you can set the microwave at the given temperature. But now microwave takes a lot less time to bake. I had made a banana cake in microwave and it was baked in only 5 minutes. So you will have to keep checking after 2-3 minutes. On induction, you can take a big pan, with a sufficient height. Pour 2-3 glasses of water and allow it to boil. Now keep the container with the batter in it such that it should not touch the water inside the pan. For that I generally use an inverted bowl inside the pan, and on the bowl I will keep the container with the cake batter. Now close the lid of pan. With the steam the cake will be baked. Also usually in my case it takes 30-40 minutes to bake in these cases. Hence you should keep checking after 30 minutes