It was not ruled out, per se, but it was not necessary. In the new science, however, rational explanation was desirable. In 1640 Ussher produced his famous calculation that the Earth was created in 4004 BC.
In 1637 Descartes produced a cosmogony that was highly influential for more than a century. It was not in their estimates of the age of the Earth - Descartes retained the biblical date.
The catastrophists (Cuvier 1812, de Beaumont 1852, Buckland 1836) accepted that the Earth was old; they disagreed with the kind of change and the rate of change that had occurred over that long history.
There was no single estimate of the Earth's age in the mid 1800's and no good way to arrive at one.
The great debate was won by the uniformitarians, so much so that the degree of gradualism was overstated and the importance of catastrophes was unduly minimized.
The modern period has been marked by an enormous expansion of the detailed knowledge of the geological history of the Earth and the processes that have acted during that history.
The attempts produced estimates from about 100 million years up to several billion years. The first is that the geological history was still being reconstructed.
If, in the year AD 1600, you had asked an educated European how old the planet Earth was and to recount its history he would have said that it was about 6000 years old and that its ancient history was given by the biblical account in Genesis.
If you asked the same question of an educated European in AD 1900 you would have received a quite different answer.
Many authors choose to present the history of a complex subject by breaking it up into major threads and following the history of each thread separately.
I have chosen instead to provide a chronology of significant works and their authors with a view to providing a sense of how perspectives on Geology changed over time.