Minimizing DFA built on set of words
There is clearly no sublinear-time algorithm; any algorithm needs to look at all words in the input to have a hope of being correct.

There is a straightforward algorithm to construct a trie that recognizes these words in linear time.  The trie is a DFA, but not a minimal DFA.

The trie is acyclic, and apparently there are algorithms for minimizing an acyclic DFA in linear time, so this yields a linear-time algorithm to construct such a minimal DFA.  See for example

Johannes Bubenzer.  Minimization of Acyclic DFAs.  Proceedings of PSC 2011.