Golden Age heroes with sidekicks sometimes used athletic team-work. The question is what qualifies as a fastball special. X might toss Y with a swinging motion rather than a javelin throw, feet-first rather than head-first.
In Star-Spangled Comics #3 the Star-Spangled Kid jumps onto Stripesy's palms and Stripsey propels him several stories high (!) with an upward motion. In #4 they catapult the Kid up to the hovering Star Rocket Racer using a tree.
I posted an instance with Blackhawk and Chop-Chop from Modern Comics #86 here.
In Justice League of America #160 the heroes' journey through time is blocked by a super-dense barrier. The Star-Spangled Kid fills Superman with star-energy and the Earth-Two Wonder Woman uses Supes as a living missing, throwing him like a javelin.
I'm thinking I'd define it as any character throwing another character at an obstacle with their permission. Wonder Woman throwing Superman in that instance would count, as would the Star Spangled Kid examples.
There are two instances I can verify with a minimum of effort.
First, dur to the Moon's lower gravity, Wolverine threw Colossus in X-Men #137.
(I'll get back to you on the second.)
I would expect the Bronze Age Hawkman and Atom did so fairly often.
I have a memory of one character (probably an X-Man) grabbing another (possibly by surprise) and administering a "fastball special." I thought that might have been from the Uncanny X-Men/New Teen Titans one-shot but its not (although that comic does contain a traditional FBS, Colossus throwing Wolverine). I also seem to think one time Wolverine might have suggest that Hulk throw him against a foe, if that sparks anyone's memory. Also, the online Marvel Database does have a "Fastball Special" entry.
I vaguely recall Carol (then Ms. Marvel) throwing Wolverine and calling it "Fastball Special, Avengers Edition" at the time when they were both members of the New Avengers.
IIRC Wolverine also threw Colossus (instead of the other way around) in the last installment of the first Proteus storyline (#129 back in 1979, perhaps).
The first FS may have been motivated by the need to rescue Banshee from a pterosaur in the Savage Land at some point circa #120.
Glomb throws Shag in the first Misfits story from Heroes, Inc. #1 (1969).
There are instances of characters throwing the Atom. Air Wave throws him in Action Comics #514. I can remember an instance from Justice League of America too but can't place it.
She-Hulk threw Wolverine against Wendigo in She-Hulk (2005 series) #16.
A Badoon threw She-Hulk at a spaceship in She-Hulk (2005 series) #26.
She-Hulk threw Hercules against the Celtic God Bran in She-Hulk (2005 series) #30.