Ds2 had severe reflux and then had sensory food issues. I tried new foods at lunch, did not make a big deal about it and then fed him what I knew he would eat at dinner so he didn't go to bed hungry. I kept a food diary to reassure myself of what he would eat.
As he got older and had started school, not every night but some nights I would give him a teaspoon of whatever we were eating, once he had that he could have his favourite foods which included white wraps. It meant he got used to taste and texture. I won't say he changed overnight but he got better.
Now he is 17 eats Indian curry, Thai curry, white fish, salmon, cheese, chicken, ham, steak, pork, bolognaise, chilli and veg, potatoes, sweetcorn, broccoli, green beans but that is about it for veg. There are foods he still won't eat like grated cheese but will eat cheese (I know) or bacon. But considering where we started he has come a long way.
At 3 it is a bit of power, distracted and wanting to be off playing etc. School helps as they see other children eating lots of different foods. Don't make it a battle, don't cajole, just put it out, eat at the same time to be sociable and chat to him as a bit of a distraction from eating. Good luck.