to answer your question I have
a year ago i had a nearly 2 year old charge who would eat NO visible veg at all. (if it was hidden in bol sauce / pasta sauce etc fine but other wise not even one pea) (when he was a baby he ate everything including all veg)
at 20 months (after about 2 months when i dont think he had had even one piece of visible vegetable (ie not even 1 pea or one bit of sweetcorn) i went back to purees and ice cubes and actually mixed veg puree in with his mash and would put it on his favourite foods. so he woudl have meat with carrot puree spread on top
I always believe in you give children food, and they can eat it or be hungry and if they dont eat nothing except water until next meal so that was what happened with 100% support from his parents.
he slowly just started to eat bits of veg cut up very tiny. peas and sweetcorn were first, then one day he just liked green beans.
He now eats almost all veg with no fuss.
also by 22 months he began understanding and if he didnt eat some veg (a single pea on a spoon or a tiny piece of carrot etc) then i didnt let him have any pudding (fruit typically followed by yogurt)
it didnt take him long to realise it was worth eating to get some yummy pudding.
once he had starting eating tiny amounts it was much easier to progress to larger amounts, so then he developed a teaste for them.
A year on he eats almost everything and is a very unfussy 2.5 year old and a joy to cook for
if you are consistent you can win