Tolkien imagined Arda to transition into the modern day as we know it, with the seventh age corresponding to the Gregorian Calendar.
In 1958 Tolkien wrote a long letter to Rhona Beare answering several questions she had posed. Towards the end, when explaining some inconsistencies between the book and our world, Tolkien explains it to the long time gap and talks a bit about the future. Estimating that another 6,000 years have since passed putting us in the sixth or seventh age.
I could have fitted things in with greater versimilitude, if the story had not become too far developed, before the question ever occurred to me. I doubt if there would have been much gain; and I hope the, evidently long but undefined, gap* in time between the Fall of Barad-dûr and our Days is sufficient for 'literary credibility', even for readers acquainted with what is known or surmised of 'pre-history'
* I imagine the gap to be about 6000 years : that is we are now at the end of the Fifth Age, if the Ages were of about the same length as S.A. and T.A. But they have, I think, quickened; and I imagine we are actually at the end of the Sixth Age, or in the Seventh.
October 1958 letter to Rhona Beare - The Letters of J.R.R. Tolkien #211
Two years later, in a writing titled "The Awaking of the Quendi & position of Ingwë/Finwë/Elwë etc.", Tolkien lengthed that time gap (to about 9,300 years), and clarified that the dates of the seventh age corresponded to the Gregorian calendar, "we being in 1960 of the 7th Age".
If they awoke in VY 1050 that would give 40 VYs, or 5,760 Sun Years in which Melkor could have dealings with them and corrupt them, before his captivity. The Atani entered Beleriand in 310 Bel. That is in the 22nd Sun-year of VY 1498. Men had then existed for 448 VYs + 22 SYs: i.e., 64,534 Sun Years, which, though doubtless insufficient scientifically (since that is only – we being in 1960 of the 7th Age – 16,000 years ago: total about 80,000), is adequate for purposes of the Silmarillion, etc.
The Nature of Middle-earth - "The Awaking of the Quendi"