The S&P 500 is a proprietary index. I am a former employee of S&P Global Ratings. (I was not a member of any S&P Index committee. I did securities ratings.) The link to the Wikipedia Standard & Poor's 500 Index article, included by OP, correctly states that:
...the components of the S&P 500 index are selected by a committee. When
considering the eligibility of a new addition, the committee assesses
the company's merit using the following primary criteria...
The criteria given in the Wikipedia article are sourced from S&P Global Ratings publically-available documentation. These are guidance criteria but the S&P 500 is not a rule-based index. The S&P 500 index committee meets and their final decision to change the index composition is kept secret even within Standard & Poor's. Only the 15 or so committee members and a very few need-to-know staff will have access to details of when and what changes the committee will make.
As stated in another answer, S&P Global Ratings issues a press release, e.g. through a wire service like PR Newswire, announcing a change in the S&P 500 index composition about 10 business days in advance. That is important, in order that index funds have time to make adjustments in order to continue to match the market performance of the altered S&P 500 index.
It wouldn't make any difference if you
were Vanguard and had a super fast computer and super fast Internet connection.
You're not going to be able to front-run the index composition change AFTER S&P makes the announcement.
Let's say you did somehow get access to the S&P 500 Index committee's decision BEFORE the official newswire announcement.
Let's say that this particular change is a major one, specifically, adding or removing a stock from the S&P 500 index, and not merely a quarterly rebalancing based on incremental changes in relative market capitalization for the 500 component stocks.
Often, such a change is anticipated by institutional money managers. That's because the index composition criteria is made available to the public (that is, all potential market participants) by S&P Global Ratings, as mentioned above. For example, it was widely and openly discussed (in the Wall Street Journal, on Twitter, etc.) and thus anticipated when Tesla stock was initially added to the S&P 500. It was due to the market cap attained by the company at that time, and the historical presence of auto manufacturers in the composition of the index.
Let's say that this particular change is not what the market was expecting. In such a scenario, if you had obtained the committee's decision in advance, that would constitute having access to material, non-public information about U.S. equity markets. If you were the Vanguard S&P 500 Index portfolio manager, both you and Vanguard's compliance department would be fully aware that acting on material, non-public information so as to profit from anticipated changes in stock price of a NYSE or NASDAQ-listed company would result in unacceptable legal and reputational risk exposures, i.e. violation of the Securities Laws of 1933 and 1940 and maybe others.
Such activity would have a high likelihood of being detected internally at Vanguard as well as by regulators--the U.S. Securities & Exchange Commission--and by compliance officials who work for NYSE and NASDAQ. Vanguard would be charged with breaking the law and maybe S&P Global Ratings would be too, as they are expected to behave responsibly and not allow something like this to happen.
That's why this scenario is NOT going to be successful if you are an index fund:
if I get a hold of the new version of the index before it is published
and buy stocks in all of the new companies, I can sell those stock
immediately after the index is published for instant profit.