When was Professor McGonagall born

It is unclear as to who this McGonagall is, though it is almost certainly the Minerva we know from the main Harry Potter series.

The Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay by J. K. Rowling only states her to be a "young Minerva McGonagall" (emphasis mine):

The class laughs. The door opens. TRAVERS, THESEUS, and four other AURORS enter, YOUNG MINERVA MCGONAGALL behind them.

Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay, Scene 64

Of course the timeline doesn't work out if this is the same Minerva from the main series as she was most likely born on the 4th of October, 1935 (as detailed in the linked question) whereas The Crimes of Grindelwald takes place in 1927/1928. We also have the scenes from 13 year old Newt and Leta at Hogwarts so from approximately a decade earlier. The film opens in 1927, 6 months after Fantastic Beasts and Where to Find Them (set in 1926), and then a further 3 months pass before the main events of the film.

EXT. NEW YORK, AMERICAN MINISTRY OF MAGIC—1927—NIGHT

Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay, Scene 1

SPIELMAN(Germanic) ... you’ll be glad to be rid of him, I expect.

PICQUERY We’d be more than happy to keep him here in custody.

SPIELMAN Six months are enough. It’s time for him to answer for his crimes in Europe.

Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay, Scene 3

EXT. OVERCAST LONDON, WHITEHALL—THREE MONTHS LATER—AFTERNOON

Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay, Scene 17


It is possible that this could be Minerva's grandmother, who she was named after, who is described as "an immensely talented witch" so could have taught at Hogwarts. Though this points to Isobel's grandmother not Robert's and so most likely wasn't a McGonagall so it is unlikely to have been her.

The birth of the young couple’s first child, Minerva, proved both a joy and a crisis. Missing her family, and the magical community she had given up for love, Isobel insisted on naming her newborn daughter after her own grandmother, an immensely talented witch.

Pottermore, Professor McGonagall By J.K. Rowling, Childhood