The first modern welfare state was the german empire, which was united 1871 but did not turn into a welfare state until three major pillars of welfare were instituted by Otto von Bismarck:
Source: Wehler, Hans-Ulrich: Deutsche Gesellschaftsgeschichte Bd.3 - von der "Deutschen Doppelrevolution" bis zum 1. Weltkrieg 1849-1914, 1995.
Would the corn dole in Rome count?
Edit - if Rome didn't provide anything but corn, would this still count as an embryonic welfare state? I've never heard of any Roman provision of health care, education, or care for the elderly? Was there any special provision for veterans of the legions?
The Islamic Empire actually had a system of Basic Income established under Abu Bakr and ended IIRC a century later. One of the five pillars of Islam is zakat, or charity, and redistribution was an institutionalized, governmental version of such a thing. Maybe by welfare state you mean something more specialized and complex than a consistent dole, but this seems like one to me. Sources: http://motherboard.vice.com/blog/guaranteeing-a-minimum-income-has-been-a-utopian-dream-for-centuries