While the Valar do "take care of it", Elves & Men (as incarnated Fea) live in time and are aware of its passage so I favor a slightly different answer to this question.
Prior to the Downfall, the way to Valinor (by sea, that is) was a straight path across Belegaer, the Great Sea. From Numenor, it took Ar-Pharazon's fleet 39 days to reach Valinor. And we are elsewhere told that Numenor was closer to Valinor than to Middle Earth suggesting that a full crossing from Mithlond (during the Second Age) might take on the order of 12-14 weeks (give or take the wind).
At the Downfall, Valinor was removed from the circles of the world, and the world was made round, but it is recorded in "The Akallabeth" that ...
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and yet the Eldar were permitted to come to the Ancient West ... Therefore the loremasters of Men said that a Straight Road must still be, for those that were permitted to find it.
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While nothing here is certain, my
Theory is that
the route to Valinor remained essentially unchanged and only the World was Bent under it.
In that case, those who were permitted to find the Straight Road, would still have a (roughly) 12-14 week crossing to Eressea and the haven of Avallone.