This is a question that is probably more about the world your campaign is located.
Dragonlance and Forgotten Realms (in numerous novels) indicate that elves at the age of 20 would appear to our eyes like human children. They grow slowly, and learn slowly. Time passes for them subjectively different then quick-paced humans.
The Player's Handbook indicates "elves reach physical maturity at about
the same age as humans," but this is not a universal conception for elves. Going with that thought though, the implication is they don't reach emotional/mental maturity at that age.
The fragile 20 year old elf may suffer all kinds of malnutrition and loss of connection from being apart from its family and homelands. Traditionally, the magic of the Elven homelands and interaction is like nourishment. The 60-100 year old elf would appear and act similar to your 20 year old characters.
You are free to make your elves however you like in your world. For instance, in the harsh climate of Athas, where to the elves the wastes are considered Elven lands (multiple editions), the starting ages for elves are 20-ish. The destructive magical cataclysm of Athas had transformed Elves significantly, forcing them to mature and grow up faster (over thousands of years).
If the question is the rules as written in the Players Handbook, the starting age is listed there:
An elf typically c1aims adulthood and an adult name around the age of
100 and can live to be 750 years old.
This is probably based more or less on Tolkien sources, adapted for game purposes (In Tolkien Elves were immortal, but suffered over thousands of years when separated from the Undying Lands).
You can choose any age for your character, which could provide an
explanation for some of your ability scores.
As to would it be weird, I give just one of a million possibilities: The elven character was plane-shifted from Athas (chose Outlander background); use these stats (no minuses in 5e, do +1 Int as per High Elf, convert everything else):
http://whinehurst.com/darksun/index.php?title=Races. [Wayback mirror]
Again, whether that is weird, also depends on your gaming world.
So for multiple reasons, the Player's handbook is giving one some artistic license here, with which a player can work with their DM and his/her game world.