Hamas

Directly? No, of course not. Were actions taken by the leadership of the state of Israel involved in the history of Hamas? Well trivially yes. But I'd strongly discourage anyone from accepting or repeating the frame in the way this question does. It feeds directly off the old antisemitic trope of Jews somehow being the secret puppet-masters behind everything that a person might find bad in the world. Stop that crap, and don't repeat it.

Hamas was created in 1987 from the Gaza branch of the Muslim Brotherhood. The Brotherhood itself, as a partially political organization, earned a rivalry with the PLO, which of course led to bloodshed between the two. At this point it appears to have been Israeli policy to not intervene, but let the two fight to weaken each other.

With the events of the First Intifada, in 1987 the Gaza leadership decided they needed an official resistance organization, and that's how Hamas was created. They got their first really big boost a couple of years later. The PLO's peace efforts culminated in the 1991 letters of mutual recognition between the PLO and Israel, which in turn led to the Oslo 1 Accord.

The problem here was that there were still Palestinians who didn't want to recognize Israel, renounce violent resistance, or have the 2-state solution pictured by the accords. Politically this created a vacuum, and Hamas was one of the groups ready and willing to fill it.

That is the story of the creation of Hamas.

Now this next bit is where we get controversial. This part of the answer really should be on the Politics site, not here, because its not settled History.

There are many within Israel who will tell you that when Netanyahu, who was originally considered a far-right politician, became Prime Minister, he in fact did not want the two state solution either. Jewish historian Dmitry Shumsky is one of them. According to this line of thinking, the policy of allowing unrestrained settlements in the West Bank, such that there can be no possible reasonable national borders there without Israeli citizens inside them, was one prong of his approach. The other was to strengthen the rift between Hamas and the Palestinian Authority (nee PLO), which necessarily meant taking actions to strengthen Hamas.

Now again, I want to emphasize that this is just one viewpoint, not some immutable accepted historical truth. You can read Shumsky's rationale in this Op-Ed in Haaretz. This is Israel's oldest newspaper, but its also an Op-Ed, which means none of the contents are necessarily vetted in any way. It could be all lies. However, I've seen it quoted and referenced around the internet, so this could be part of where people are getting this idea that Hamas somehow owes its existence to the government of Israel.