This is a pretty tricky question, so there will be even more others can say beyond my contribution. You are correct that the basic formula of a flatbread with things on top are pretty common in many different culinary traditions and that may be a good stepping off point to challenge the premise of your question. Did pizza as we know it "come from" another foodstuff or did Italians develop a tradition of baked breads with toppings contemporaneously? To be frank, I cannot answer that question and would be surprised if someone can offer the first novel 'invention' of such baked breads which then radiated out to be further localized in Italian pizza. My instinct is to keep in mind that like all cultural artifacts, food is often shaped by both the people producing it and the larger context of the world they live in. As such it is not unthinkable that even if the notion of baking something adjacent to pizza was learned by Italian bakers, they likely would still claim - with some credibility - that it was their invention. As such, we should probably address the city which claims this authority - and nigh all other authority relevant to pizza! - Naples.

The Neapolitan claim to the invention of pizza stretches back into antiquity, well before Marco Polo's journey in the thirteenth century. The consensus as I understand it is that Italian bakers in the various separate cities and polities in early modern Italy were baking bread that was both broadly similar (yeast fed dough with ample olive oil and additives) but also intensely localized variations on what can generally be called focaccia. I am hesitant to even write that word, though, because the claim to who made this bread first and who makes it best can be...an intense discussion to say the least. Regionalism in Italy is difficult to overstate in the modern day - well after unification - and even more so in the early modern period. That said, there is some evidence that the first pizza-adjacent food was a kind of Neapolitan 'galette' which roughly translates to a flat cake or pie. These would not have been sweet dishes in their seventeenth century iteration, but likely would have been savory with additives like olives, cheese or fish. A more clear 'invention' of modern pizza in Naples would come with the Pizza Margherita pioneered by Raffaele Esposito in 1889. The story goes that Esposito, a prominent Neapolitan baker, baked a pie for Queen Margherita of Savoy, consort of the sovereign of a newly united Italy which served as a decidedly Neapolitan expression of patriotism, adorned in three ingredients which served as signifiers of the Italian red, white and green tricolor: tomato sauce, mozzarella cheese and garnished with basil. The queen liked the pizza so much that it became a kind of national food, a signifier of the cultural unification of a previously disunited peninsula.

That is a nice story but reality is more complicated. As I mentioned earlier we know that pizza or pizza adjacent breads have been made since antiquity well outside of Italy and there are many regional variations on pizza. While the Neapolitan pizzaiolo has been vaunted to the highest reaches a lowly artisan can achieve in relatively recent history, there is a real problem in claiming that pizza as we know it was invented in 1889: we know people were baking focaccia and other breads with additives under different names all over Italy well before Italy was unified. At what point is it focaccia and and what point is it pizza? At what point do these seemingly unimportant linguistic hangups break down entirely? In Sicily, a common Christmas and feast day foodstuff called sfincione is focaccia topped with tomatoes, breadcrumbs and anchovies. Now a Neapolitan may well want to bring bodily harm down upon you for calling that pizza: it's focaccia. Of course, when Italian immigrants moved to the Americas en masse in the nineteenth and twentieth centuries the close knit communities (often by necessity) meant that regional food ways which would have otherwise been separated by hundreds of kilometers were now side by side. If you go to any New York pizzeria worth going today your guaranteed to find two slices on hand and ready to order by the slice. One is the New York style pizza which was derived from the Neapolitan style but made with greater access to meats, cheeses than would have been available to most working class bakers in Naples and also cooked in generally colder ovens. The other is a square pie called a "grandma" or "Sicilian" slice which very much resembles sfincione but with, again, much easier access to the meats and cheese that were so precious in the Old World. Somehow after moving to the Americas, focaccia seemingly became pizza!

So all of this brings me to my real point on the semantics of pizza: what even is pizza? To offer a definition that is, perhaps, too broad I would classify pizza as a wet dough, cooked in a relatively hot oven with various regional and traditional toppings and additives. Furthermore, even if the idea of how to cook this way originated in the Middle East or East Asia, I'm inclined to view those flatbreads as something distinct and say that pizza has been - without a doubt - most influenced by working class Italians and those in the vast diaspora of Italians in the nineteenth and twentieth century. The technique, ingredients, procedure and consumption vary wildly from region to region and from city to city to this day with most modern culinary 'refinement' of the form coming from Naples. That said, I do think the most important element here is why these questions are so slippery to historians in the first place: the absence of written sources which illuminate these questions. Most cookbooks were written by relatively affluent professional artisans who worked for royalty in the early modern period and the first truly significant mention of pizza in the modern context is as a culturally patriotic foodstuff served to the first Italian royals. For that reason, the working-class nature of bread baking, often done communally with the intention to be sold cheaply, has evaded the primary sources in which historians derive most of their evidence. As such pizza was, as it is now, something that is profoundly shaped by the individuals and communities that make it and difficult for us to assess the 'origin of' in any overly broad quality.