I think that if you want to support all verbs, you face at least 3 'ambiguities' whether you first check the first, second, or third character of the string. (It must be at most the third, as the shortest verbs are 3 characters long.)
First checking the first character is ambiguous between POST, PUT and PATCH. First checking the second character is ambiguous between HEAD, DELETE, and GET. First checking the third character is ambiguous between GET, PUT, OPTIONS, and PATCH. [0]
edit As danachow points out, the verbs are not all used with the same frequency. If real-world performance is the goal we'd presumably want to optimise for the GET case, which presumably means first checking the first character, as the 'G' is unique to GET.
[0] https://developer.mozilla.org/en-US/docs/Web/HTTP/Methods