tolkiens legendarium - How old is Middle-earth?

I'm surprised that there isn't a duplicate for this.

This question about plate tectonics in Middle-earth got me thinking, that it is probably not old enough to have the lands shaped by geological processes. (As others explain in the answers that it not how middle earth was formed)

Generally, geological processes like mountain ranges rising take millions of years.

I tend to get confused about the early history of Arda, I believe there was a time before it existed as a physical world.

How long has Middle-earth existed as a physical entity?

Answer

There is an answer in Quora here. It's a nice summary, so I'm sharing it below.

To quote The Annals of Aman:

It is computed by the lore-masters that the Valar came to the realm of Arda, which is the Earth, five thousand Valian years ere the first rising of the Moon, which is as much as to say forty-seven thousands and nine hundred and one of our years.

That divides into 3500 Valian years (or 33,530 of our years) before the creation of the Two Trees, the 'Days without days'. Then 1495 years of the Trees (14,322 of our years), 'the Days of Bliss'. Then five years (48 of our years) of Darkness.

Total 5000 Valian years or 47,901 solar years from the Creation to the rising of the Sun and Moon.

The rest of the First Age was 590 solar years, the Second Age was 3441 years and the Third Age was 3021 years.

Grand total, up to the end of Lord of the Rings, 54,953 solar years.

In a letter written in 1958 Tolkien said that he imagined the gap between "the fall of Barad-dûr" and "our days" to be about 6,000 years.

Which would make Arda 60,000 years old, give or take a millennium.

That's from the most complete and detailed timeline Tolkien made, in the late 1950s. During the 1930s he was imagining the timescale to be about 20,000 years shorter.

By the 1960s he was of the mind that he should write that the universe was 14 billion years old and Arda itself 4.5 billion years old, and the whole story of its creation by the Valar, Varda making the Stars long after the Earth itself was made, and the origins of the Sun and Moon, was merely a Númenorean myth — but he never fleshed out this idea in detail.

You can find the mentioned script in The History of Middle-earth, Vol. X: Morgoth's Ring, Part Two.

Also, Tolkien changed his mind constantly. He invented languages and drew maps and etc. It's natural that you feel confused.