This is a historical analysis of the subject, as such, it deserves its own topic. I'm using several sources. By using different sources of good to high quality, my aim is to create a historical explanation based on convergence of evidence—the idea that difference sources supporting the argument makes for a much more robust case.

I quote the passages I deem most relevant. Also, in order to boost credibility, I give a Media Bias/Fact Check profile about factuality of the each main source.

The Japan Times — Israel's historical role in the rise of Hamas

MB/FC Profile — Factual Reporting: High

The international focus on the war in Gaza has helped obscure the fact that Israel in the 1980s aided the rise of the Islamist Hamas as a rival to the secular Palestinian Liberation Organization and its dominant faction, Yasser Arafat’s Fatah. Israel’s policy was clearly influenced by the U.S. training and arming of mujahideen (or Islamic holy warriors) in Pakistan from multiple countries to wage jihad against Soviet forces in Afghanistan.

(...)

Hamas, for its part, is alleged to have emerged out of the Israeli-financed Islamist movement in Gaza, with Israel’s then-military governor in that territory, Brig. Gen. Yitzhak Segev, disclosing in 1981 that he had been given a budget for funding Palestinian Islamists to counter the rising power of Palestinian secularists. Hamas, a spin-off of the Palestinian branch of the Muslim Brotherhood, was formally established with Israel’s support soon after the first Intifada flared in 1987 as an uprising against the Israeli occupation of Palestinian lands.

Israel’s objective was twofold: to split the nationalist Palestinian movement led by Arafat and, more fundamentally, to thwart the implementation of the two-state solution for resolving the protracted Israeli-Palestinian conflict. By aiding the rise of an Islamist group whose charter rejected recognizing the Israeli state, Israel sought to undermine the idea of a two-state solution, including curbing Western support for an independent Palestinian homeland.

Israel’s spy agency Mossad played a role in this divide-and-rule game in the occupied territories. In a 1994 book, “The Other Side of Deception,” Mossad whistleblower Victor Ostrovsky contended that aiding Hamas meshed with “Mossad’s general plan” for an Arab world “run by fundamentalists” that would reject “any negotiations with the West,” thereby leaving Israel as “the only democratic, rational country in the region.” Avner Cohen, a former Israeli religious affairs official involved in Gaza for over two decades, told a newspaper interviewer in 2009 that, “Hamas, to my great regret, is Israel’s creation.”

(...)

Israel, by contrast, persisted with its covert nexus with Hamas. With the consent of Israel, Qatar, a longtime sponsor of jihadi groups, funneled $1.8 billion to Hamas just between 2012 and 2021, according to the Haaretz newspaper.

Israeli Prime Minister Benjamin Netanyahu, who has been in power for much of the past decade and a half, told a meeting of his Likud Party’s Knesset members in 2019 that, “Anyone who wants to thwart the establishment of a Palestinian state has to support bolstering Hamas and transferring money to Hamas,” adding, “This is part of our strategy — to isolate the Palestinians in Gaza from the Palestinians in the West Bank.”

The Intercept — Blowback: How Israel Went From Helping Create Hamas to Bombing It

MB/FC Profile — Factual Reporting: Mostly Factual

But did you also know that Hamas — which is an Arabic acronym for “Islamic Resistance Movement” — would probably not exist today were it not for the Jewish state? That the Israelis helped turn a bunch of fringe Palestinian Islamists in the late 1970s into one of the world’s most notorious militant groups? That Hamas is blowback?

This isn’t a conspiracy theory. Listen to former Israeli officials such as Brig. Gen. Yitzhak Segev, who was the Israeli military governor in Gaza in the early 1980s. Segev later told a New York Times reporter that he had helped finance the Palestinian Islamist movement as a “counterweight” to the secularists and leftists of the Palestine Liberation Organization and the Fatah party, led by Yasser Arafat (who himself referred to Hamas as “a creature of Israel.”)

“The Israeli government gave me a budget,” the retired brigadier general confessed, “and the military government gives to the mosques.”

“Hamas, to my great regret, is Israel’s creation,” Avner Cohen, a former Israeli religious affairs official who worked in Gaza for more than two decades, told the Wall Street Journal in 2009. Back in the mid-1980s, Cohen even wrote an official report to his superiors warning them not to play divide-and-rule in the Occupied Territories, by backing Palestinian Islamists against Palestinian secularists. “I … suggest focusing our efforts on finding ways to break up this monster before this reality jumps in our face,” he wrote.

They didn’t listen to him. And Hamas, as I explain in the fifth installment of my short film series for The Intercept on blowback, was the result. To be clear: First, the Israelis helped build up a militant strain of Palestinian political Islam, in the form of Hamas and its Muslim Brotherhood precursors; then, the Israelis switched tack and tried to bomb, besiege, and blockade it out of existence.

(...)

“When I look back at the chain of events, I think we made a mistake,” David Hacham, a former Arab affairs expert in the Israeli military who was based in Gaza in the 1980s, later remarked. “But at the time, nobody thought about the possible results.”

The Times of Israel — For years, Netanyahu propped up Hamas. Now it’s blown up in our faces

MB/FC Profile — Factual Reporting: High

For years, the various governments led by Benjamin Netanyahu took an approach that divided power between the Gaza Strip and the West Bank — bringing Palestinian Authority President Mahmoud Abbas to his knees while making moves that propped up the Hamas terror group.

The idea was to prevent Abbas — or anyone else in the Palestinian Authority’s West Bank government — from advancing toward the establishment of a Palestinian state.

Thus, amid this bid to impair Abbas, Hamas was upgraded from a mere terror group to an organization with which Israel held indirect negotiations via Egypt, and one that was allowed to receive infusions of cash from abroad.

(...)

Most of the time, Israeli policy was to treat the Palestinian Authority as a burden and Hamas as an asset. Far-right MK Bezalel Smotrich, now the finance minister in the hardline government and leader of the Religious Zionism party, said so himself in 2015.

According to various reports, Netanyahu made a similar point at a Likud faction meeting in early 2019, when he was quoted as saying that those who oppose a Palestinian state should support the transfer of funds to Gaza, because maintaining the separation between the Palestinian Authority in the West Bank and Hamas in Gaza would prevent the establishment of a Palestinian state.

While Netanyahu does not make these kind of statements publicly or officially, his words are in line with the policy that he implemented.

The same messaging was repeated by right-wing commentators, who may have received briefings on the matter or talked to Likud higher-ups and understood the message.

Reuters — EU's Borrell says Israel financed creation of Gaza rulers Hamas

MB/FC Profile — Factual Reporting: Very High

EU foreign policy chief Josep Borrell said on Friday that Israel had financed the creation of Palestinian militant group Hamas, publicly contradicting Prime Minister Benjamin Netanyahu who has denied such allegations.

Opponents of the Israeli government and some global media have accused Natanyahu governments of boosting Gaza rulers Hamas for years, including by allowing Qatari financing of Gaza.

"Yes, Hamas was financed by the government of Israel in an attempt to weaken the Palestinian Authority led by Fatah," Borrell said in a speech in the University of Valladolid in Spain without elaborating.