As stated in the question, I am interested in learning when the Cold War was 'effectively' won. Did either or both parties recognize that the war had been won / lost?
What were the events major turning points that signaled that the US had won?
This runs into a few fairly common issues in pop-history and how history is often presented and interpreted that I think are interesting to talk about.
Namely this idea of inevitability: in the case of WW2 1943, and particularly the victory at Stalingrad are typically cited as the turning point of the war and that from this point onwards, as you say, the war was "effectively won" by the Allies. The reasons for this are simple: the Axis had lost the strategic initiative and the cost of changing the tide would be increasingly costly while the ability to pay any cost would be diminishing. It is in this regard that their defeat seems "inevitable" or that the allies had "effectively won". But this is a bit of what we might call "historical determinism", the idea that the final outcome of history is basically predetermined. The essential flaw with this outlook is that it robs all actors of their agency. While unlikely (and I should emphasize that it is very unlikely), it certainly was still possible for the Axis to have won or in the very least to have gotten a negotiated peace in WW2. It would have taken a degree of brilliance on the part of the axis and incompetence on the part of the allies but it certainly was a possibility.
I say all this to preface and say that determining that a conflict was "effectively won" or "effectively over" is an assertion that can really only ever be made with the benefit of hindsight, and even then I'd argue it does warrant some qualifiers. With all that said I would say that the safest time to cite as the "effective victory" of the cold war would have been about 1988/89.
Let me explain: From the late 60's onwards the USSR would increasingly lag behind the United States economically. The reasons for this are numerous and complex and I'd point you u/Kochevnik81's answer for a more detailed breakdown of the Soviet economy towards the end of the cold-war. But the important thing here is that the USSR, while lagging further and further behind the US economically was not in danger of imminent collapse until very, very late in the game. While there were many cracks showing in the soviet system there were also many part parts of the foundation that were strong (or at least: appeared to be). Had Gorbachev not come along it would not be hard to imagine the USSR middling along for several more decades, but alas he did. Gorbachev's reforms had a two-pronged effect for destabilizing the eastern bloc.
Firstly: Glasnost, a policy of increasing openness which allowed for more transparency and more frank discussion (and criticism) of the Soviet system. This effectively made it easier for people to protest and organize against the eastern bloc governments (even in eastern bloc countries where this policy was not official, this soviet policy emboldened many in the eastern bloc). Couple this with Gorbachev's greater unwillingness to use force to quash public opposition (not wanting a repeat of 1956 or 1968) in the eastern bloc and domestically meant that movements to break away from the USSR would have a much higher chance to succeed.
Secondly: Perestroika, which was an attempt to reform the lagging Soviet economy. This push for reform was needed for the long-term stability of the USSR but the reforms themselves were less than successful. Boiling down a massive and complicated topic to the basics for this: Perestroika effectively dismantled/destabilized the ailing economic systems of the USSR but did not effectively replace them with better (or even equally good) systems. This caused the economy of the USSR to start to tank which naturally had a ripple effect on the economies of the eastern bloc.
So what we've got here in the late 80's in the east is a quickly deteriorating economic situation and an increasing ability to criticize, protest, and organize against the government. These are prime conditions for counterrevolutions. But note that though these policies began in 1986 and 1985 respectively, I don't list the "effective victory" as happening until 1988/89, the years of the eastern bloc revolutions. And this reason for this harkens back to what I said earlier about inevitability. While Glasnost and Perestroika ultimately caused the collapse of the eastern bloc, had they been done differently they just as easily could have saved it. China is a functioning example of a communist state preserving itself through reform (not only preservation but making it stronger than ever) and it was certainly possible for glasnost and perestroika to have done this for the USSR... if the policies and programs themselves were better. While the eastern bloc lagged in many ways it still had the power and organization to potentially rejuvenate itself, and while this would be difficult it was certainly not an impossibility (once again: see modern China).
But the reality is that the reforms weren't better and would help to wither away the states of the east. While admirable in their goals their implementation was ultimately incredibly flawed. Thus only when the issues with the communist system came to a head in 1988 and the eastern bloc governments began to collapse would I say the West had "effectively" won. The USSR had started to actively lose ground it had held since the beginning of the conflict and regaining that ground would become increasingly costly while simultaneously the USSR would be increasingly unable to afford any costs at all. The Cold War was declared over at the Malta Summit in 1989, and would completely end with the collapse of the USSR in 1991. It might be a lame answer but I really couldn't comfortable say the Cold War was "effectively over" earlier than 1988.
Hope this answers your question and perhaps more importantly: gives a bit of insight into how we view history itself.