Midnight Tears is a good option for delayed effect
What is a bit unclear to me is why you do not know what the Constitution DC for the poison is. Poisons in 5e have a clearly defined effect, and a set save DC, so there should be no question what they need to roll to make the save, and what happens, if they do not.
If this is a poison from the rulebook, and there is an actual defined effect of the poison, then you should have let that effect happen. Actions have consequences, and it is not as if you did not give him several extremely clear warnings that drinking it is a bad idea. Also, in 5e, poison often does not "straight out kill" a PC -- save or die is a concept that 5e moved away from for the most part. Here is the effect of one of the most deadly poisons published for 5e, Purple Worm poison:
A creature subjected to this poison must make a DC 19 Constitution saving throw, taking 42 (12d6) poison damage on a failed save, or half as much damage on a successful one.
That is, even if they fail their save, if this kills them outright depends on how many hits they have. Only if after losing all their hits the remainder is as large or larger as their hit point maximum, they will die outright from massive damage. Else they just drop to 0 and are dying, with plenty of time for their group to stabilize or heal them. And even if they die, a group of 5th level can have access to spells like revivify, so even that might not be the end of the character.
If you designed the encounter and just noted down the poison for yourself as a "potent poison" to figure out what it would do later when the players use or identify it, you have to do that now. What you make the poison do in this case is up to you. You could take a slightly less deadly poison, Midnight Tears in particular seems like a good match for your delayed effect (using the Con save you already had them pre-roll):
Midnight Tears (Ingested). A creature that ingests
this poison suffers no effect until the stroke of midnight.
If the poison has not been neutralized before then, the
creature must succeed on a DC 17 Constitution saving
throw, taking 31 (9d6) poison damage on a failed save,
or half as much damage on a successful one.
You can find the list of "official" poisons on p. 257/8 of the DMG.
P.S. As an aside, as long as it is not annoying the other players, I do not think you need to disincentivize the goblin player from eating random things -- to me it is a fun way to characterize the unwise, curious character. You only need to demonstrate that their decisions can have consequences, and that maybe, they need to be a bit more careful with this if they do not want a repeat experience.