Where are James, Lily and Snape during the Fantastic Beasts movies? Are they at Hogwarts or are they still too young to be at Hogwarts?
They weren't even born yet
Fantastic Beasts and Where to Find Them takes place in 1926 and Fantastic Beasts: The Crimes of Grindelwald takes place in the following year, 1927.
EXT. SOMEWHERE IN EUROPE—1926—NIGHT
Fantastic Beasts and Where to Find Them - The Original Screenplay
EXT. NEW YORK, AMERICAN MINISTRY OF MAGIC—1927—NIGHT
Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay
On the contrary Lily, Snape and James were all born in 1960, a lot later than the Fantastic Beasts films we've seen so far.
The headstone was only two rows behind Kendra and Ariana’s. It was made of white marble, just like Dumbledore’s tomb, and this made it easy to read, as it seemed to shine in the dark. Harry did not need to kneel or even approach very close to it to make out the words engraved upon it.
JAMES POTTER LILY POTTER BORN 27 MARCH 1960 BORN 30 JANUARY 1960 DIED 31 OCTOBER 1981 DIED 31 OCTOBER 1981 The last enemy that shall be destroyed is death.
Their births are even the same going by film canon.
That doesn't mean we won't see them though as we know these films are already playing fast and loose with the timeline. For example, they changed Minerva McGonagall's birthday/age.
They won’t exist yet at any point in them.
It has been stated by JKR that the Fantastic Beasts series will be from the years 1926 to 1945.
This is most likely because the war with Grindelwald, which is the topic of this series, ended in 1945 when Dumbledore defeated Grindelwald.
“Considered by many the greatest wizard of modern times, Professor Dumbledore is particularly famous for his defeat of the dark wizard Grindelwald in 1945, for the discovery of the twelve uses of dragon’s blood and his work on alchemy with his partner, Nicolas Flamel.”
- Harry Potter and the Philosopher's Stone, Chapter 6 (The Journey from Platform Nine and Three-Quarters)
James and Lily Potter were both born in 1960, fifteen years after the stated conclusion of the Fantastic Beasts series.
“James Potter, born 27 March 1960, died 31 October 1981
Lily Potter, born 30 January 1960, died 31 October 1981
The last enemy that shall be destroyed is death.
Harry read the words slowly, as though he would have only one chance to take in their meaning, and he read >>the >last> of them aloud.”
- Harry Potter> and the Deathly Hallows, Chapter 16 (Godric’s Hollow)
James and Lily’s birth dates remain consistent with the years given in the books in the movies as well.
NEW ANGLE - HARRY
As he stares at the tombstones of his parents:
JAMES POTTER LILY POTTER Born 27 March 1960 Born 30 January 1960 Died 31 October 1981 Died 31 October 1981 “The last enemy that shall be destroyed is death.”
Hermione appears, looks at Harry. Sees that tears are streaming down his cheeks. Hermione raises her wand, traces a circle in the air and a WREATH of CHRISTMAS ROSES blossom in the snow. Harry nods, staring at them.
- Harry Potter and the Deathly Hallows, Part 1 (Screenplay)
Snape was in the same year at Hogwarts as James and Lily, therefore he must have been close enough in birth to them to be eleven years old at the same time they were.
“Severus was very interested in where I went every month,’ Lupin told Harry, Ron and Hermione. ‘We were in the same year, you know, and we – er – didn’t like each other very much. He especially disliked James.”
- Harry Potter and the Prisoner of Azkaban, Chapter 18 (Moony, Wormtail, Padfoot and Prongs)
Snape also is shown with Lily at the Sorting ceremony in the movie, so presumably he’s in the same year with them in the movies as well. Though he likely is, even if he is not in the same year as James and Lily, he cannot be more than seven years apart from them in age since their attendance at Hogwarts overlaps. It would not be possible for him to have been born before or during 1945 and still have his Hogwarts years shared with James and Lily’s.
318... we emerge from the darkness of the SORTING HAT, sitting upon a stool in the candlelit Hall, House tables aglow with a sea of rapt faces.
Two boys -- SIRIUS BLACK and JAMES POTTER -- sit together at the Gryffindor table, watching as...
A YOUNGER McGONAGALL sweeps the hat from the stool and calls out a name. James Potter watches Lily smile nervously at the boy next to her (Snape), then rise and make her way to the top of the Hall. As McGonagall lowers the hat over Lily’s brow, James watches intently, waiting. Finally, McGonagall speaks and all those around James CHEER. He merely smiles, watching Lily approach. He gives Sirius a nudge, to move over, making a space for Lily. As she takes her seat, she glances across the hall to the boy, who watches impassively as James reaches out his hand to introduce himself to Lily.
- Harry Potter and the Deathly Hallows Part 2 (Screenplay)
Therefore, unless either JKR breaks with established canon in the Fantastic Beasts series (which she has proved willing to do) or extends the timeline of the series to include later years, James, Lily, and Snape should not appear anywhere within the Fantastic Beasts series because they would not be born yet.
The first Fantastic Beasts movie was set in 1926. The Crimes of Grindelwald was set in 1927.
The dates above come from Pottermore, however, since Pottermore no longer exists, the Pottermore Wiki links are the best I could source for the birthdays.