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Imagine Bob the elf who is a passenger on the ship travelling to Evermeet from the Neverwinter harbor (sailing from the Material Plane to the Feywild).

Captain of the ship is an elf who already sailed to the Evermeet, so this journey is possible.

So Bob goes to the captain and asks him “How much time would it take?”

How would the captain answer?
Is it possible to give such an answer at all? Or maybe the journey time would vary from time to time?
Is it possible to estimate the time units here? Days? Weeks? Months? Years? Decades maybe?

The rules are a bit ambiguous, but it probably has a Material Plane location

Evermeet is mentioned in three of the 5e books.

Far Traveler Background

The fabled elven islands far to the west are home to elves who have never been to Faerûn.

"Far to the west" seems to imply a physical place on the same plane that the captain could give an estimate for the time to travel to.

Sword's Coast Adventurer's Guide

Evermeet is mentioned in quite a few places in this book. First it is provided as a location in the quote:

Off the western coast of Faerûn are a number of island realms of varying size. The most distant, and yet perhaps the most symbolically important to the mainland, is Evermeet, the island paradise of the elves...

Then later it is elaborated on by a second-hand account (which references the legends):

I overheard it said by the captain of the ship that Evermeet now somehow straddles all three planes: our world, the Feywild, and Arvandor. It touches them all, but exists fully in none of them...

If this account is to be believed, we still have Evermeet with a connection to the Material Plane that could likely be sailed to.

Later in the book in the Elves section we get:

or set sail across the Trackless Sea to the isle of Evermeet.

...lending further credence to the idea that it is a physical destination.

Mordenkainen's Tome of Foes

This is the most recent book to lend information about Evermeet, and it says:

Millennia later, Evermeet still exists, although now it is unmoored from the world, somewhere in the space between the Feywild, Arvandor, and the Material Plane. By using secret pathways, entering a fairy ring on special nights, or traversing a moonlit sea by following certain stars, elves of many worlds can get to Evermeet — if they’re lucky. Even from Faerûn, for instance, one can sail to Evermeet only on a ship captained by an elf who has been there before.

This reinforces the rumor the writer in Sword's Coast Adventurer's Guide mentions, but says nothing to remove the presence of a Material Plane island (or part of an island). Only that it shares a presence in other planes as well. While sailing to it involves taking advantage of some special method, it probably still has a physical route on the Material Plane to get there (even if magic gets in the way of normal sailing there).

Mythals

It is possible that the level of presence of Evermeet in the Material Plane is contingent on a mythal as there is a line in Mordenkainen's Tome of Foes which says:

The elves left for Evermeet upon the order of their leader, who commanded the wizards of the city to alter the mythal so that evidence of the empire’s existence was wiped from the surface of the world.

Mythals are some of the most powerful magic present in the Forgotten Realms lore, so it would make sense if a Mythal was involved with the difficulty of navigating to the island.

If you're willing to use lore from older editions, you can get a reasonable answer, but even using a 5th edition map, the answer is "quite some time." Per that map, the distance from the Moonshae Isles to Evermeet is unknown but certainly further than 500 miles. The Moonshae Isles themselves are around 400 miles from the Sword Coast region. If you decide to consult the 2nd edition Forgotten Realms Atlas (and ignore the fact that Faerun's dimensions have changed considerably over the years), you come up with a distance of roughly 1200 miles from the Moonshaes to Evermeet, or about a 1600 mile trip.

Setting aside the fact that this particular journey will be partially planar, and assuming no more than incidental magic is used, you can estimate travel time in one of two ways- check the DMG for ship sailing speed and divide your distance by the number you get, or look around for a real-world equivalent. Using the first method (p. 117 says a sailing vessel can travel 24 hours a day, p. 119 gives an average speed of 2 mph) we end up with 1600/48 = 33 days, or about 4.5 weeks (or three tendays and change, depending on the calendar you use).

A quick Google search for the second method tells me that a Transatlantic crossing during the Age of Sail was about 3400 miles (about twice the distance we're looking for) and took 6 to 8 weeks, so a reasonable estimate for the trip using a real-world equivalent is 3-4 weeks. This coincides nicely with our estimate from the first method.

Given that you'll have quite a bit of wiggle room with the actual distance involved, due to changing editions and planar magic, and a similar amount of play with the sailing speed due to sorcery and magic vessels, a curious passenger wouldn't need to know all that. Were I a captain asked how long it would take to sail to Evermeet, I'd say "Weather permitting, about 30 days." It's close enough for a casual response.