Some trace modern day Baptists to the Anabaptists, while others to the English Separatists. I tend to favor the latter, the English Separatists. But I want to fast-forward a bit to when Baptists began to formulate their confessions, the General Baptists (Arminians) on the one hand and the Particular Baptists (Calvinists) on the other.
In their respective confessions neither the General Baptists or the Particular Baptists new anything about Dispensationism and its approach to eschatology, in particular. In fact, for the Particular Baptists, who patterned their confession (Second London Baptist Confession of 1689) according to the Westminster Confession of Faith, they were covenant Baptists.
We may safely trace the begins of Dispensationalism as we know it today to the early nineteenth century Plymouth Brethren in England.
But today, many Baptists have Dispensational eschatology as part of their doctrinal statements. In fact, to be a member of certain Baptist churches you have to hold to dispensational premillennialism in all its glory.
However, the first Baptists were not dispensationalists and neither are all Baptists, which includes yours truly.