The following stories show that the inverse square law was widely discussed at the time of Newton.
First story is about Hooke. He wrote to Newton proposing to determine "how a point will be moving under the inverse square law". Specifically he discussed the example of an object
with some initial velocity (NOT directed towards the center) how would it move if the Earth
did not offer any resitanace. Newton's answer was INCORRECT (he wrote it will move on a spiral winding towards the center of the Earth). In the next letter Hooke wrote the correct answer: it will move on an ellipse. (Hook did not have a mathematical proof of this: he probally EXPERIMENTED!)
To this last letter Newton did not reply. Several years later Sir Christopher Wren in a conversation with Hooke and Halley (in a pub:-) proposed to prove that the inverse square law of attraction would imply Kepler orbits, and offered a reward for a proof.
Halley passed this to Newton, and Newton replied that he has a proof.
But he could not find it among his papers. Some time later he sent to Halley a manuscript with a "proof". This is what later become Principia. (It is still discussed whether Newton's proof was a valid one. I share the majority opinion that it was. However, WHEN did Newton obtain it remains a mystery. Certainly he did not know the result, not speaking of the proof at the time when Hooke wrote to him. Later Newton spread rumors that he knew it almost from his childhood:-).
Halley proposed to mention Hooke in Principia. But Newton stubbornly resisted, and his angry answer to Halley is well known and documented.
The whole story is told in many places, one of them is Arnold's book, Barrow and Huygens,
Newton and Hooke. Unlike some other stories told by Arnold this story is true, and is well documented: I read the corresponding letters of Newton and Hooke myself.
And everyone can check this in the published collection of Newton's correspondence.
Conclusion. The Inverse square law was discussed at the time of Newton as a plausible CONJECTURE. Newton proved it.