Yes

Readying a spell involves (PHB p.193):

When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell’s magic requires concentration (explained in chapter 10). If your concentration is broken, the spell dissipates without taking effect.

For a spell that relies on targeting a creature we look at p.204:

A Clear Path to the Target

To target something, you must have a clear path to it, so it can’t be behind total cover.

The spell has a clear and unambiguous target to which you have a line of effect when you cast it - the prospective "first goblin". You would also need a line of effect when you release the energy. The fact that the target only exists potentially does not make it an invalid target. The spell requires a creature to target: a creature has been provided.

Also, time is not an barrier to magic, see the whole of the Divination school.

I'm going to do something unusual here, and suggest that you ignore the official rules, just a little. Bear with me.

The official ruling: unclear, but unlikely

The PHB states that when you Ready the action Cast A Spell:

...you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs

which implies that you cast the spell immediately, meaning that you can't target "the first goblin to walk round the corner" because you can't see it at that point.

Targeting vs. casting

One important thing to note is that the PHB does not state that you have to choose a target at the moment the spell is "cast". It says that you must have a clear path to the target when you target them, and many spells further stipulate that you must be able to see them, but nothing clarifies what part of "casting" involves selecting a target.

Rules as intended: a brief speculation

Personally, I don't think that the intent of these rules is to further limit what a spellcaster can ready. I think that the above excerpt is intended to explain that holding your spell until a trigger is a concentration process that can be interrupted and lose you the spell slot. I think that the phrasing "cast it as normal but hold its energy" is a poor choice of words, and probably wasn't meant to use the word cast as a keyword linked to the idea of targeting the spell. I suspect that the rules about spells and targeting forgot to take the "cast-and-hold" of readied spells into account, and thus didn't clarify how it works. Sage Advice has said that you choose the target of a Readied Attack when you take the attack, so I don't see why it would be different for a spell.

Rules as fun (and fair): I say YES

My interpretation of the above excerpt is that readying a spell readies the magic in the same way that an archer might draw their bow and hold it. The word "cast" is being used to mean "the magic is drawn up from whatever source you use, and brought into the world", as an explanation for why the spell slot is lost if you lose concentration before the trigger. I would rule that the magic is just drawn and held - it's shaped into the spell when the trigger happens, and it's that shaping that I would refer to as "casting".

In D&D 5th Edition, spellcasters can cast cantrips as much as they like. This is important, because in earlier editions, they couldn't, and it became a running joke that at low levels a character could be a wizard in the morning and a light crossbowman in the afternoon. In 5e, casters are meant to be able to use their magic like a fighter uses a sword: reliably. If an archer says "I Ready an action to shoot the first goblin" they can't see the goblin at that moment, but any DM would let them target it when they see it. Not allowing spellcasters to do something similar would be to handicap them unfairly - they're already at a disadvantage because they have to hold concentration, while the archer holding their bow drawn doesn't.

No. (Sadly, for casters.)

Whie I'm not happy this is the rule, the rule's there: the Ready action draws a clear distinction between readying any other action and readying the casting of a spell.

In the case of any other action, Ready talks about "the action you will take in response to [the] trigger." (PHB p.193, "Ready", emphasis mine) So in most cases you complete all elements of the action as part of your reaction in response to the trigger. In the case of the Attack action the first step--again, taken after the trigger as part of your reaction--is to choose a target. So there's no problem choosing the goblin as a target after it's come into view.

Contrast that with the case of a spell being cast: Ready specifies that it is cast at the time of the Ready action, but that its effects (only) are held using your concentration. We know you burn the spell slot at the time of Ready because expending the slot is part of cating the spell. By the same logic you must target the spell at the time of Ready, too. (For what it's worth, Jeremy Crawford says via Twitter that targeting is "an organic part of casting a spell and rarely isolatable." Thanks to @Danikov for the pointer.)

Note that all of the above is in reference to a spell that targets a creature, as in the original question. Spells targeting a point in space that is a legal target at the time of the Ready action can be triggered by the appearance of a creature. In other words, you can Ready a fireball to scorch the goblin as it comes out of the cave, but not a witch bolt.

Yes, a target can be chosen when the spell is unleased.

This part is exactly the same as making a melee or ranged attack. On PH p. 194, the first step to making an attack is "Choose a target." Choosing a target is as much a part of making a ranged attack, as it is casting a targeted spell.

Yes, there are limitations to what targets are valid for certain spells, which don’t apply to weapons. But the mechanic is the same: take an action to ready your attack, a valid target comes into view, choose the target, resolve the attack. In either case, the action requires a target which may not be available when the action is readied.

Of course, there are differences between readying a spell and readying an attack with a weapon. These are delineated in the last paragraph of the "Ready" section (PH p. 193). (The spell must have a casting time of 1 action. The caster must end concentrating on another spell, if any. The caster may lose a spell slot, if concentration is broken.)

Nothing seems glossed over in the “readied spell” description: the restrictions are sketched out with some elaboration — but there’s nothing regarding targeting in these restrictions. Targeting is covered by the general rule on readied actions.

A spell’s requirements are accounted for when it is completed.

The requirements of a spell are generally accounted for at the completion of a spell being cast. For example, spell slots are expended when the spell is completed.

When you cast a spell with a casting time longer than a single action or reaction…if your concentration is broken, the spell fails but you don’t expect a spell slot or scroll.

PH p. 202, Longer Casting Times

(A readied action works a little differently than this, in that the spell slot is consumed if the spell is interrupted.)

Don’t get hung up on the one phrase Cast a Spell

The argument against this position pretty much hinges on the interpretation of the meaning of "casting a spell." But this term is used pretty loosely in the rules.

The specific mechanics are for various situations are typically laid out (for when spell slots are expended, or not, etc.) Pay a mind to the descriptive text about what happens when spell is cast in various situations. Levy those prices, but not more.

The requirements of spell casting are clearly laid out. Don’t assume there are more, hiding in between the lines.