Further, he says that the idea of a welfare state or government wealth redistribution did not exist in Greek or Roman society

Have you ever heard of the phrase "bread and circuses"? Or, in its original Latin, "panem et circenses"? This was written in 100AD by a Roman poet Juvenal:

Already long ago, from when we sold our vote to no man, the People have abdicated our duties; for the People who once upon a time handed out military command, high civil office, legions — everything, now restrains itself and anxiously hopes for just two things: bread and circuses

This refers to a practice which started about 250 years earlier (about 140 years before Jesus was born), where Roman politicians would provide free grain and put on games, to influence the votes of the people. It may not have been a welfare state, per se, but in the 250 years since the practice started, the provision of free grain to the lower classes of Rome had become standard practice - to the point that there were riots if the grain allowance was stopped or even reduced (often in times of famine or war, when the supply of grain decreased).

And, this started in a city with no significant Jewish influence, and before Christ was born.

he says that the idea of a welfare state or government wealth redistribution [...] comes from Judaism.

If that's true... why did it take so long to be implemented? The welfare state didn't start until about 100 years ago.

Australia was one of the first countries to implement a government-funded pension scheme for elderly people and disabled people, in 1908. (Germany was the first, in 1889.)

Similarly, the first country to introduce unemployment benefits was the United Kingdom, in 1911 (with Australia following suit more than 30 years later).

If the welfare state truly comes from Judeo-Christian thinking, then why did it take so long to arise? Christianity had existed for about 1,900 years before the first pension schemes arose, and Judaism had existed for much longer. What took them so long?

Ancient history may not be my specialization, but as an academic historian, perhaps I can offer some contribution to the discussion. First of all, the term "Judeo-Christian" is an invention of the 1930s, (initially used to promote a more inclusive American social model intended to combat antisemitism), gaining particular traction in American social discourse only in the 1990s, during the so-called "culture wars." Applying it to ancient history is problematic at best. Secondly, the Romans were not strangers to state-organized redistribution of wealth. Some of the earliest examples include Tiberius Gracchus' Lex Sempronia Agraria (133 BC), a massive agrarian reform program which entailed a redistribution of land that had been conquered by the Roman military, but then was illegally held by aristocratic Roman families. An excess amount of this land was then confiscated by the state, and then redistributed to destitute Romans, which turned a onetime underclass into tax-paying, military-serving stakeholders in the Roman republic. The aristocrats were then compensated from state coffers for their alleged "losses." Tiberius Gracchus' brother, Gaius, supported broadening these measures, while also using the state to secure grain from North Africa, which was then rationed to Roman plebeians at what amounted to a below-market prices (the Lex Frumentaria). This insulated the poorest of Roman society against market fluctuations of a basic life necessity. These efforts, of course, were far from a nineteenth century idea of a "welfare state," but they do demonstrate the Roman state's deliberate intent to manipulate resources to improve the lot of the poorest in society.