From the site you posted
Gandalf to Frodo:
" Let me see - it was in the year that the White Council drove the dark power from Mirkwood, just before the Battle of Five Armies, that Bilbo found his ring. A shadow fell on my heart then, but I did not know yet what I feared. I wondered often how Gollum came by a Great Ring, as plainly it was "
So right from the start (2941) Gandalf rules out the lesser rings. Its therefore either one of the 7, or its the One. The 7 are supposedly all accounted for, although we never here the full story. So lets assume they are an outside chance.
Many years later, he and Aragorn spend years looking for Gollum, to try and get some gen on the origin of the ring. Without success.
Gandalf at the Council of Elrond:
"And then again in my despair I thought again of a test that might make the finding of Gollum unnecessary. The ring itself might tell if it were the One. The memory of words at the Council came back to me: words of Saruman, half-heeded at the time. I heard them now clearly in my heart.
"The Nine the Seven and the Three," he said, had each their proper gem. Not so the One. It was round and unadorned, as it were one of the lesser rings; but its maker had set marks upon it that the skill, maybe, could still see and read."
This suggests Gandalf hadn't been paying attention in class. He has only to spot the absence of a gem, to know its not one of the 7, and therefore it is the One. This meeting of the White Council is probably 2953 (the last one, where Saruman asserts the Ring has rolled into the sea).
It then takes 48 years for Gandalf to 'suspect' according to Appendix B. His suspicion is aroused by Bilbo's longevity, and unwillingness to relinquish the ring. He starts to do something in 3001: the search for Gollum.
The hunt for Gollum takes 16 years. In 3017 Gandalf talks to Gollum and reads Isildur's scroll.
He arrives in Hobbiton in April 3018 and throws the ring into Frodo's fire. Now he knows with absolute certainty.
Lets all pause for a moment and admire the thoroughness of Gandalf's research..... before noting that a bit of logic and paying attention at the White Council would have got him to the same conclusion fully 65 years earlier.
Gandalf Greymantle, not Gandalf Greymatter.
So again this seems to be a bit of an issue in the books.... Made a 1000 times worse by the fact that Gandalf does a bit of a battle with Sauron.