A strange short sentence with 就
漢典 就〈副〉(6)


  用在动词前面，表示在某种条件或情况下自然怎么样。
  [without…there can be no]
  如：不斗争，就不能前进。


《现代汉语词典》Page 697 ❼ 副 d)
also shows some examples.



There is not problem about the Chinese explanation above.
就 is an adverb here.
However, I would say, "after...then..." or "because...then..." for the English translation.
After A happened, then B happened.
Because A ..., B then ....

会议之后，许多人都认为班农的策略是在发疯。然后特朗普就赢得了选举。

After 许多人都认为班农的策略是在发疯. And, 特朗普 then 赢得了选举.
After many people thought that the strategy of Bannon was crazy, (and) Trump then won the election.

Because 许多人都认为班农的策略是在发疯, 特朗普 then 赢得了选举.
Because many people thought that the strategy of Bannon was crazy, Trump then won the election.