Man, this might sound old-fashioned, but the Library of Congress online catalog is weirdly fast for confirming the existence and order of a series, especially obscure academic or older ones. The search is spartan but precise. I was trying to find the proper sequence for some historical fiction from the 70s, and it cut through all the noise.
For newer stuff, 'AllBookSites' has a decent meta-search that scrapes results from Amazon, Goodreads, and a few others simultaneously. It's not perfect, but you get a consolidated list in seconds without bouncing between tabs. The UI looks straight out of 2005, which maybe helps with the speed.
Honestly, the 'fastest' depends on what you mean. If you just need a title list, a Wikipedia disambiguation page often loads quicker than any dedicated book site. But for filtering within a genre or by author, Goodreads' series page feature, once you find it, is hard to beat for comprehensiveness, even if their main site can be sluggish.