Greetings! This is a great question on one of those curious events of the Cold War, and it certainly is one which can be a bit surprising to first-time students of the Suez Crisis! In this response we shall explore why the US seemed to go against its Western European allies in the Crisis, as well as how the crisis impacted the US overall in the lens of the Cold War "superpower" rivalry. Let's begin.

The first and most obvious thing to understand is that the US had been involved in the Suez before its nationalisation by Egyptian President Gamal Abdel Nasser on the 26th of July 1956. Most notably, the US feared that the Egyptian President would lean more towards the Soviet Union, as Nasser had already arranged arms deals with countries in the Soviet bloc and was already beginning to emerge as the champion of Arab independence from the former colonial masters of Britain and France. The British and French were, ostensibly, more concerned about the possible loss of prestige and power in the region which would arise from Nasser's growing influence, but the Americans were more preoccupied with the Soviet threat which Nasser's Egypt seemed to be inviting into the Arabian peninsula. US Secretary of State John Foster Dulles, who was attempting to improve relations with the Arab nations, then retracted the US' offer of aid to build the Aswan High Dam on the 19th of July, 1956. This retraction was viewed as a rejection of Nasser's willingness to cooperate with the American and Soviet spheres of the Cold War simultaneously, and the retaliation of nationalising the Suez struck a massive blow to the British and French interests.

We have to understand, at this point of the response, that the American foreign policy in the Middle East was filled with contradictions and complications. On the one hand, its anti-imperialist stance was closer to the sentiment of Nasser and Arab freedom parties in the region, whilst on the other its support for Israel was seen as a thorn in the side of many Arab governments as well. Historian Matthew A. Fitzsimons on this curious mix of interests which Washington had:

"It [the US] sought friendship and oil from the Arab states and outraged Arab sentiments by its espousal of Israel; like Britain, it professed a sympathy for Arab nationalism and in its anti-imperialism was closer to the nationalist temper of the Arabs; like Britain, its former and future ally, it was interested in the stability of the Middle East, but its anti-imperialism worked against the survival of the indirect British Empire in the region."

When the nationalisation of the Suez came, a peaceful solution was imperative: the American government could not risk turning the Middle East into an active battleground, and its Israeli ally had already aggravated Egypt in previous years with incursions into Gaza. Two London Conferences followed suit, and Nasser was approached several times with proposals to "joint administration" of the Canal Zone, but to no success. It was not particularly helpful that US-UK relations in the Suez were strained due the poor rapport between US Secretary of State John Foster Dulles and British Prime Minister Anthony Eden. The former wanted to distance the US from "old-world" colonialism in a post-colonial age, and the latter wished to maintain a hold of the Suez (but could not do so without American support). In a rather revealing comment made on the 2nd of October, Dulles commented:

"The Suez Canal...is not an area where we [the United States, Britain, and France] are bound together by treaty...There are other problems where our approach is not always identical. For example, there is in Asia the so-called problem of colonialism. Now there the United States plays a somewhat independent role...and that makes it impractical for us, as I say in every respect to identify our policies with those of other countries on whichever side of the problem they find their interests."

The United States, in sum, was unwilling to get tangled up in "colonial adventures" in an age where economic influence and indirect support were the new tools of diplomacy and sphere-building. Thus when the Israelis invaded on the 1st of November and the Anglo-French forces joined in (as per a secret agreement) on the 5th, Washington immediately levied consequences upon its Western European allies. Rather famously, President Dwight D. Eisenhower exclaimed to his British counterpart upon learning of the British invasion:

"Anthony, are you out of your mind?"

It was also a contributing factor that the British had conducted their agreement for military intervention with the French and Israelis in secret, without Washington's approval (or indeed knowledge) of the whole venture. Alongside backing a United Nations Resolution to agree to a truce, the US applied an oil embargo on Britain and France, the first time in history that oil had been used as a political weapon. With the supply of oil from the Suez already having been blocked by Egypt after the invasion, the embargo crippled Anglo-French oil reserves, and the value of the pound sterling dropped alarmingly without the support of the dollar (a fitting analogy for the political side of events in Suez). US Ambassador to the United Kingdom Winthrop W. Aldrich, writing about his role in the Suez Crisis, summed up the position of Eisenhower's government rather aptly:

"The effect on our Government of this sudden and unexpected British and French move and of the actual opening of hostilities on Egypt two days later was catastrophic. The British Government had been told over and over again at the highest levels that we wished to do everything possible to avoid the use of force, and for force to be used without any warning came as a profound shock."

So with that part of OP's query covered, let us then turn to this curious "final question":

"was the Suez crisis the opportunity for the US to declare that it is the new world leader?"

In the sense of the Western world, yes. The Suez Crisis marked the end of the British and French Empires of old, and served as a "nail in the coffin" of the old-order world of European imperial powers. Britain and France had been "relegated" to relying on US support for economic and diplomatic matters, and Eden's weakness in his negotiating position during Suez was proof of such reliance. It did not however, serve as a tool for the US to proclaim itself as the "world leader" in terms of the Cold War. The USSR under Khrushchev had also protested the Anglo-French-Israeli invasion, and the Soviet premier had famously "waggled his rockets", threatening nuclear strikes on London, Paris, and Jerusalem if the crisis was not de-escalated immediately. Because these threats were made public, and the US' opposition was not, it entered the Soviets into a new role as the supporting superpower of Arab nationalism, and marked a new, more invested phase, of the Kremlin's activities in the Middle East. It was also unhelpful that the invasion coincided with the Hungarian Revolution's crushing in Europe, which the US was unable to get involved in (for reasons I discuss in more depth here).

Hope this brief response helped, and feel free to ask any follow-up questions on the Suez Crisis as you see fit!