There's no definite one way to go, though I prefer to have characters know each other. Here's some options and what you get of it:

Total strangers

How well does this work? Well that depends on whether your players are all willing to buy into "a group of strangers will work together as a team in life and death situations". It's a trope that makes up a lot of 80s action-adventure films and pulp stories.

On the other hand, when you hear about groups that devolve into thieves stealing from people and paladins going fanatical on their teammates, it's when the group DOESN'T buy into that idea.

Heard of each other

"Ah, you're the Red Sword, I know of you!" etc. Not quite as bad as total strangers, but again, it depends on the group of players deciding to make their characters align in interest - the difference here is that with some assumed character knowledge about the other characters, you have more reason to trust them or want to work with them.

Work for a similar faction/cause

The characters all work for a similar group or cause, and so they've definitely heard of each other and have social reason to work together. This is where most games that rely on mission-based play do well in coordinating a group.

Personal ties

Each character knows either 1 or 2 of the other characters personally. So, everyone in the group knows at least one of the others, but not everyone knows each other personally. This still has the potential pitfall of conflict, but usually works better for bringing characters together without too much pretense.

Full-fledged group

An established group that has worked together before and at least a decent working relationship with each other. You can either have players state what that is to each other. It could be relatively new ("We banded together 2 months ago, so we're still figuring each other out, but we know we can depend on each other with our lives") or it could be after much time ("10 years of adventuring off and on together") and so on.

If the expectation is for the party to work together (and in most D&D, it is) let the players know and figure out what feels good for them with that understanding in mind.

5E Realms lore does not specifically address this. 4E Realms lore, on the other hand, does. Their exact origin is subject to some debate, even among the elves.

Collectively, the elves are known as the Tel’Quessir⁶ ("The People"), a title that encompasses Eladrin, Wood Elves, High Elves, Sea Elves, and so on. It is 'widely accepted' that the Tel’Quessir are native to the Feywild¹. It is believed that they first immigrated to Abeir-Toril over a hundred millenia ago, while the exact date is uncertain it is believed to have been prior to −24,000 DR, with some manuscripts indicating it was as early as −30,000 DR, the same time in which dragons were setting up their empires (Note: Source on this is from AD&D)⁴. The Wild Elves were the first to arrive.¹

The exact origin of the Elvish race is subject to some debate. Some ancient manuscripts suggest that they were the result of a battle between Gruumsh and Correlon that occurred in the Feywild. During said battle, Correlon was injured and his shed blood became the Eladrin.². Other types of elf, not liking the superiority this implies in that the Eladrin are the first and 'purest' of elves, disagree with this theory³. Another theory postulated is that since the Feywild tends to be a 'reflection' of the Prime Material Plane, and thus produces creatures that are echoes of creatures from the Prime, it is also possible that the Elves are one such echo... though what, exactly, they would be an echo of is uncertain¹.

Perhaps also worthy of mentioning is the current in-lore explanation for how the Feywild (also known as Faerie) is treated according to current lore. The Feywild was created as it exists today, a 'lighter' echo of the Prime Material Plane. It was made by Primordials in the far distant past, before recorded history begins.⁵

For a while, the Feywild existed alongside the Prime and interaction between the two was common. But, at some point in ancient history, the two drifted apart and travel between them became increasingly difficult². This is the explanation for why, in prior editions of D&D, the Feywild didn't "exist" in the Forgotten Realms. It was out there, you just couldn't get to it.

The Spellplague (the event that 'kicks off' 4E in the Realms) changed that, reshuffling the cosmology to drag the Feywild back into close proximity, and placing it in the accessible location it resides in today⁵.

Checking through published 5E Realms material, it does not contradict any of this... the 5E Realms cosmology is essentially the same as the 4E Realms cosmology, and the lore established within 4E is considered to hold true in 5E, except where directly overridden. And even then, the changes are usually justified in-lore (such as the array of gods and goddesses getting rejiggered due to Ao meddling with them).

The primary lore sources we have in 5E Realms are the Sword Coast Adventurer's Guide, the DMG, and published adventures. None of these go into detail on the origins of the Elves, or even on the specific nature of the Feywild... thus we may assume the lore of older sources hold true.

Sources

¹ Brian R. James and Ed Greenwood (September, 2007). The Grand History of the Realms. (Wizards of the Coast)

²Bruce R. Cordell, Ed Greenwood, Chris Sims (August 2008). Forgotten Realms Campaign Guide. (Wizards of the Coast)

³James Wyatt (December 2007). Dragon 361: A Fractured Family. Wizards of the Coast.

⁴Steven E. Schend and Kevin Melka (1998). Cormanthyr: Empire of the Elves. (TSR, Inc) NOTE: AD&D source

⁵Dungeon Master's Guide 4th edition. (Wizards of the Coast)

⁶Kim Mohan ed. (2015). Sword Coast Adventurer's Guide. (Wizards of the Coast)