I can understand it, that a lot of Jewish people from all around the world came to Israel and started speaking in their second language to their descendants so that their offsprings became native speakers of Hebrew. But how did they recreate the phonology of the language? If so many people came there with a plethora of other tongues, how come that their native languages' phonology didn't influence Hebrew phonetically?
Jews all over the world had still been reading Hebrew out loud in services long after it had ceased being the daily language of any of them and Jewish scholars had been comparing these pronunciations for centuries
This meant that there were several living liturgical phonologies to draw from. Ultimately, Modern Israeli Hebrew is largely based on the earlier Yerushalmi (Jerusalemite) Sephardi pronunciation (qamatz gadol and patakh are merged, there is no distinction between taw and thaw), albeit with an Ashkenazi accent. This Ashkenazi influence led, in particular, to the loss of aleph and ayin, the merger of khet and chaf and the guttural resh. It's often claimed that the guttural resh is German/Yiddish influence, but this is hard to prove. The masoretes of the early middle ages in the near east actually record that resh is pronounced in two distinct ways, one like trilled at the front of the mouth as in Sephardi pronunciation, and one more guttural as in Ashkenazi pronunciation. It's entirely plausible that the Ashkenazi pronunciation simply generalised the guttural pronunciation (as Sephardi did the trill) rather than starting from a Sephardi-like trill and then adopting the German guttural r
Actually, the native language of original speakers did influence the resulting phonology. This page explains some of those influences. For example, pharyngeals are lost in populations that lived in communities that did not have pharyngeals, and there is variation between [w] and [v] among speakers, related to the dominant language of their place of origin. The main problem is determining what the "uninfluenced" state was, that is, at what point did Hebrew cease being the first and dominant language of a large enough population, and then what are the pronunciations facts of that version / those versions of Hebrew. That was almost 2 millenia ago.