user15543: A quaint question I had lately: what is the earliest known appearance of the “Fool’s Mate”? I refer to both the name and the move sequence.
A quick search with Google Books revealed a reference dated to 1672 in The famous game of chesse-play by  Arthur Saul and John Barbier.
Here is an image of the relevant text portion.

Transcript:

Of a Mate to bee given at two Draughts.
CHAP. XX.
Meeting with an eaſie Gameſter, thou mightſt likewiſe give him a Mate at two draughts, if he ſhould chance to play thus: Firſt, to remove his Kings Biſhops Pawne, a ſingle draught (which I told thee before, was ill to play for the firſt draught) thou thy Kings Pawne, a ſingle remove: he for his ſecond draught, his Kings knights pawn, advanced a double remove: thou bringing forth thy Queene, into the Fifth Houſe of thy Kings Rooks file, giveſt him Mate at thy ſecond draught: which Mate for him that hath it given him, may well (if the ſchollers Mate, be cal’d the peſants Mate) be termed the fools Mate.


user27180: In reference  @Rewan Demontay's answer, I know that Augustus, Duke of Brunswick published Das Schach- oder Königsspiel under the pseudonym Gustavus Selenus in 1616. I can't confirm that this work actually mentions Fool's Mate (I don't speak German, and I can't find the full text in online references) or that there is no earlier reference.

user15543: By a stroke of luck, Tim Krabbe mentioned an earlier occurrence on his site. It is in his AD Magazine issue #135 entitled "LOYDS MOOISTE VERGISSING,", meaning "LOYDS MOST BEAUTIFUL MISTAKE."
In Dutch: "Wit en Zwart helpen elkaar daarin om tot een mat te komen, zoals in het snelst mogelijke mat vanuit de beginstelling, het Narrenmat (1.f3 e5 2.g4 Dh4 mat). Al in 1616 noemde Gustavus Selenus dit mat, dat in een normale partij nauwelijks kan voorkomen."
In English, this means " White and Black help each other to arrive at a mate, as in the fastest possible mate from the starting position, the Jester mat ( 1.f3 e5 2.g4 Dh4 mate). Gustavus Selenus called this mat as early as 1616, which can hardly occur in a normal game."
Now we have a reference to 1616 and the name Gustavus Selenus, although I am unable to trace it.
Addendum 11/8/2021: In an earlier comment, @Hauke Reddmann issued a Google Books link to "Schachkompositionen: Die besten Aufgaben und Komponisten der Schachgeschichte. Mit über 500 Rätseln und Lösungen". On page 25 information is given that makes the book an additional source.

15543: <p>A quaint question I had lately: what is the earliest known appearance of the “Fool’s Mate”? I refer to both the name and the move sequence.</p>
<p>A quick search with Google Books revealed a reference dated to 1672 in <em><a href="https://www.google.com/books/edition/The_famous_game_of_chesse_play_London_16/5sFjAAAAcAAJ?hl=en&amp;gbpv=0" rel="nofollow noreferrer">The famous game of chesse-play</a></em> by  Arthur Saul and John Barbier.</p>
<p>Here is an image of the relevant text portion.</p>
<p><a href="https://i.stack.imgur.com/rNQaJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/rNQaJ.png" alt="Screenshot of facsimile reproduction of book" /></a></p>
<p>Transcript:</p>
<blockquote>
<p><em>Of a Mate to bee given at two Draughts.</em></p>
<p><strong>CHAP. XX.</strong></p>
<p>Meeting with an eaſie Gameſter, thou mightſt likewiſe give him a Mate at two draughts, if he ſhould chance to play thus: Firſt, to remove his Kings Biſhops Pawne, a ſingle draught (which I told thee before, was ill to play for the firſt draught) thou thy Kings Pawne, a ſingle remove: he for his ſecond draught, his Kings knights pawn, advanced a double remove: thou bringing forth thy Queene, into the Fifth Houſe of thy Kings Rooks file, giveſt him Mate at thy ſecond draught: which Mate for him that hath it given him, may well (if the ſchollers Mate, be cal’d the peſants Mate) be termed the fools Mate.</p>
</blockquote>
 27180: <p>In reference  @Rewan Demontay's answer, I know that Augustus, Duke of Brunswick published <em>Das Schach- oder Königsspiel</em> under the pseudonym Gustavus Selenus in 1616. I can't confirm that this work actually mentions Fool's Mate (I don't speak German, and I can't find the full text in online references) or that there is no earlier reference.</p>
 15543: <p>By a stroke of luck, Tim Krabbe mentioned an earlier occurrence on his site. It is in his <a href="https://timkr.home.xs4all.nl/admag/index.htm" rel="nofollow noreferrer">AD Magazine</a> issue #135 entitled <a href="https://timkr.home.xs4all.nl/admag/helpmat.htm" rel="nofollow noreferrer">&quot;LOYDS MOOISTE VERGISSING,&quot;</a>, meaning &quot;LOYDS MOST BEAUTIFUL MISTAKE.&quot;</p>
<p>In Dutch: &quot;Wit en Zwart helpen elkaar daarin om tot een mat te komen, zoals in het snelst mogelijke mat vanuit de beginstelling, het Narrenmat (1.f3 e5 2.g4 Dh4 mat). Al in 1616 noemde Gustavus Selenus dit mat, dat in een normale partij nauwelijks kan voorkomen.&quot;</p>
<p>In English, this means &quot; White and Black help each other to arrive at a mate, as in the fastest possible mate from the starting position, the Jester mat ( 1.f3 e5 2.g4 Dh4 mate). Gustavus Selenus called this mat as early as 1616, which can hardly occur in a normal game.&quot;</p>
<p>Now we have a reference to 1616 and the name Gustavus Selenus, although I am unable to trace it.</p>
<p><strong>Addendum 11/8/2021:</strong> In an earlier comment, @Hauke Reddmann issued a Google Books link to <a href="https://books.google.de/books?id=ccAuBQAAQBAJ" rel="nofollow noreferrer">&quot;Schachkompositionen: Die besten Aufgaben und Komponisten der Schachgeschichte. Mit über 500 Rätseln und Lösungen&quot;.</a> On <a href="https://books.google.de/books?id=ccAuBQAAQBAJ&amp;pg=PA25&amp;lpg=PA25&amp;dq=%22gustavus+selenus%22+%22narrenmatt%22&amp;source=bl&amp;ots=PUNMa2Xio3&amp;sig=ACfU3U03keen-0r00-hILY1CfUS0IBoABw&amp;hl=de&amp;sa=X&amp;ved=2ahUKEwiiuuSen9PvAhUIKuwKHU6RAJEQ6AEwAHoECAEQAw#v=onepage&amp;q=%22gustavus%20selenus%22%20%22narrenmatt%22&amp;f=false" rel="nofollow noreferrer">page 25</a> information is given that makes the book an additional source.</p>
