The overarching belief, at least from what we can tell, is that Israel tolerated Hamas's precursors at a minimum, and supported it at a maximum. What that means depends on how you want to delve into it.

A lot of this comes from reporting and information that came to light for most only about a decade ago, despite Hamas's formation over three decades ago. The general gist is this: Israel tolerated Hamas by allowing its predecessor organizations, and Islamism in general, to flourish among Palestinians. The reasons depend on who you ask.

Some of the more...I'd argue, conspiratorial takes are that Israel allowed Hamas to flourish and/or financed it in its early stages because Israel was attempting to provide a scapegoat with which to persecute Palestinians. Ignoring how absolutely difficult it would be to not only pull of an operation of this type, it lacks a bit of common sense. After all, Israel was fighting the PLO at the time that Hamas precursors were popping up, which was still hijacking planes internationally and carrying out terrorist attacks on Israelis broadly. It seems strange to argue that Israel would "create" a group to oppose Israel when they already had a group opposed to them, carrying out the types of attacks they would expect Hamas to carry out, at least in those early days.

Hamas's early roots and growth tell a different story, I'd argue. Hamas's roots in the Muslim Brotherhood follow the tale of many similar groups. Much of their operating began as a provider of social services; charities, universities, Islamic education, and the like. Israel, during this period, was aware of the leadership origins of the Muslim Brotherhood branches that were flourishing there. It even had some general fears about them, particularly the spiritual leader and founder of Hamas, Sheikh Ahmed Yassin. However, while some raised the alarm about Yassin, calling him an ideologue who was dangerous to strengthen, Israel appeared to tolerate and work with his social organizations, though the question of financing is unclear (some allege Israel gave finances, others do not believe or deny it). In the early days, this meant giving licenses to operate as a provider of social services, or to establish universities, or to build mosques; hardly what you'd expect of a terrorist organization.

Israel's more likely goal, as explained by some Israeli officials later on in news reports on the subject (when this finally came to light to many in the West), was to create an Islamist alternative to the secular PLO. This would have two benefits:

1. The Islamist groups operating there did not appear to be violent towards Israel, or opposed to its existence. In fact, they seemed downright friendly, compared to the secular PLO. It was hoped, or at least perhaps blindly optimistic folks believed, that the Islamist movement would turn out to be peaceful and provide an alternative to the violent secularist movements in the PLO.

2. Even if there was not to be this peace, a second benefit would be to divide the Palestinian movement, and weaken the secular PLO. As I mentioned, the PLO was at the time carrying out attacks on Israel, and the idea of weakening it seemed great. The Islamist groups seemed interested in violence only against the secularists, so it is not surprised that Israel saw this as an opportunity.

By the time Israel wised up to what was actually happening, it was too late. These ostensibly peaceful groups, which Israel had turned a blind eye to, began to take on more militant tones in the mid-80s. Yassin, who had capitalized on Israel's optimism, now seized an opportunity to use the movement he had established to try and take leadership of the "Palestinian resistance" away from the PLO, and into his own hands. This did not begin with Hamas, but rather with predecessor organizations. Fatah, a member of the PLO (really the head group of it), tipped Israel off (ironically enough) to Yassin stockpiling weapons in 1984. Israel raided the location, found the weapons, and arrested Yassin. But Yassin stuck to his excuses and scripts: he claimed that the weapons were for fighting Fatah, not Israel, so they let him go. Alarm bells started ringing for Israeli intelligence, but too late; the stockpiles were, of course, growing as a way to fight Israel too, and they were waiting for the right moment to start. The First Intifada, which began in 1987, provided the perfect context; the movement was seen as grassroots and separate from the PLO, and Hamas could use its position on the ground and among popular sectors of Palestinian society to launch itself formally in 1988 and start carrying out attacks.

So when the question comes down to it, did Israel create Hamas? Absolutely not. That would entail actually taking action to found and organize the group.

Did Israel tolerate Hamas? Not really, but it did tolerate Hamas's predecessors, who it believed were focused on fighting Israel's other enemies, who were also attacking it. As to why, it's likely the result of as I said, Israel's blind optimism to some extent, and also its desire to weaken the secular Palestinian groups...who ended up, in a bit of a shock, starting to signal they were willing to renounce violence and accept Israel's right to exist the very same year that Hamas was formally founded. That's not to say that if Israel hadn't tolerated Hamas, it wouldn't have arisen either; we can't know that, and many speculate it would've since Islamism was on the rise regardless, and Israel would have been powerless to stop it. That's also not to say that if Israel hadn't tolerated Hamas, then its only enemies would have remained the PLO, who ostensibly renounced violence in 1988 and formally in the Oslo Accords in 1993, since we also don't know what would have happened there (i.e. would other groups have taken up the mantle, or would Hamas still have formed?).

But Israel, today, seems to have understood that it tolerated groups and movements that grew right under its gaze, and failed to predict what they would truly become, and that intelligence failure is actually a fascinating one for discussing what happens when a state thinks it can control popular movements and their spread.