How to make my pizza dough Soft?

If you've added 250ml of milk for 1.5KG of flour then your dough is way too dry, there isn't nearly enough moisture for any kind of bread dough. A typical traditional pizza base recipe uses a ratio of about 5:3 flour to liquid by weight, meaning you'd need about 900ml of liquid for the dough. You've also added milk powder, which also needs to be hydrated, so add about 30ml or so for that as well. If you are using all purpose (plain) flour you should add a bit less water, say 10%, as there's less gluten in it.

When you add the liquid to the flour it's going to be sticky, very sticky in fact, but that's bread making and you can't avoid it. You can oil your hands but that doesn't last, you're better off removing your rings and just cleaning your hands later. As the water incorporates and is absorbed the dough will get less sticky, but pizza dough is going to stay a bit sticky even after it's been kneaded enough, it will then be much less sticky after the first rise.

The recipe you have isn't any kind of pizza base recipe I've ever heard of, milk, milk powder, eggs and sugar are all enriching agents and the dough you'll get isn't going to have the kind of structure you're looking for in a pizza base unless you're looking for some sort of non-traditional brioche style. It's also going to take much longer to rise as these ingredients slow the process. Traditionally a pizza base is flour, water, yeast and salt with olive oil being optional (I put it in).

That recipe is so far from what most cooks would consider a pizza recipe¹, that I am ignoring the unusual ingredients for now.

What is blatantly obvious is the hydration² - 250 ml of milk plus an egg for 1.5 kg of flour means around 20%. This won’t give you a workable yeast dough. The standard pizza recipe is somewhere between 60 and 80%, depending on the kind of pizza crust and the types of flour used. This website gives a nice comparison of the different types.

If you want to salvage the current batch, you will have to gradually incorporate around 500-700 ml of water and yes, this will initially get you to a “solid bits in muddy liquid” stage. It would be easiest if you could dump it in a stand mixer. First it will be a lump sloshing around in water. After a while, the lumps should gradually soften and the dough becomes even. Work in batches, if necessary, not all mixers can deal with this much dough. If you are working by hand, use a large bowl for the initial “mushing” and later you can go back to the bench.
General advice: Don’t let “sticky” dough tempt you to constantly flour the bench, you’d be throwing the ratios again. Rather learn about different kneading techniques, some are great for soft dough.

¹ A standard pizza recipe is “flour, water, salt, yeast and (optional) oil”. Use good quality ingredients, very little yeast and lots of time. Your is some kind of enriched dough, which I would expect for other things like challah, sweet buns, ...

² Hydration or Baker’s Percentage is the percentage of liquid with the flour as base unit. Your average bread dough will be around 60% and 65%, bagels can be as low as 50% and going over 70% brings you into high-hydration territory where regular kneading won’t work too well. Find an overview here.