My understanding is that the crew was close to mutiny, not because they were starving, but because they did the math and there was not enough supplies to make it back to Europe if they went much further west. That is, they were approaching the point of no return.
The most critical supply - fresh water - was easily replenished for the home journey.
Not sure what they would have used for food - presumably dried fruit and dried slated meat were not difficult to make. (How easy is salt to come by? Would their original supplies have left them a good amunt, or was it preserved in salt water not crystals?)
Moderator Note
The question in the OP isn’t how the world would be different if Central America didn’t exist. The question, although phrased with an unrealistic hypothetical, is really about how far Christopher Columbus could have sailed before getting himself and his crew into trouble.
This can be factually answered and verified by looking at the historical data that we have for the expedition. We know the size of the ships. We know how large the crews were. Christopher Columbus had a journal with a lot of information in it. There is a lot of information about the ships and what they carried in historical texts.
Let’s focus on the actual factual question here, not the silly hypothetical framing of it, please.
Hey!
I was aware that a missing Central America would change a lot of things besides how far Columbus would have gotten before everyone dying. I hadn’t realized that the crew would have mutineed before they got far enough to risk that. And came really lose to doing just that.
I was thinking about how, with the way things are, anyone who sailed from Europe or Africa would just about have to hit the Americas, as long as they had enough food and water
Chances are the ships would first come upon the Marquesas islands and or any of the many islands of French Polynesia first which spans over a 1000 miles in the S Pacific. The crew might be chewing leather and eating barnacles by then but it’s a couple weeks sail from mexico to the marquesas.so doubtful imho they would’ve starved. Maybe they’d hang out in the Solomon Islands or New Zealand.
They were literally sitting in oceans of the stuff. Well, they’d have had to evaporate the sea water, but that was likely a well-known technique.
If Columbus sailed due west from his original landing place, and managed to miss the Bahamas and, for some reason, no one drew in Mexico on the map, and he continued uninterrupted due west into the Pacific, he’d be passing north of Hawaii after 8,000 km [say 5000 miles], and then basically missing everything until he crashed into Taiwan at about 16,500 km.
Someone upthread said Columbus sailed about 10 miles per hour, which would be a max 400 km per day, so with the most optimal conditions they were more than a month to Asian coast landfall. If they weren’t sailing due west then there is even more empty ocean in other directions. They had no Polynesian navigator-prince of the calibre of Tupaia whom Cook had on board, and no handy early blocking out of major landmasses by the Dutch to help, and no Polynesian navigational lore about how to spot islands over the horizon. They were floating dead meat.
And if they chanced on an island would they be met happily with laes and complimentary drinks? When post-Mutiny Bligh was making a similar journey, but in a rowboat, they were starving but, after having one man killed when they first stopped for supplies, they declined to land on other Pacific islands because of their fear of attack.
One example of a New World crop is peppers (i.e., capsicums). I decided to dry some peppers myself once. I didn’t do any research on how to do it, and didn’t have any experience drying any other fruit or vegetable, and did it entirely by guesswork. They came out great, the first try.
I don’t think preserving plant foods is all that difficult. Meat is a little trickier, but meat is meat, and all the same techniques used for Old World meats would work for New World meats, too.
Another point is that Columbus fudged his numbers (as well as his false assumption) to make the distance shorter. Presumably the officers - and so the crew - knew what numbers he was saying in the courts of Europe, and when they would have exceded that distance.
IIRC, the incorrect answer Columbus took from the alternative facts of ancient Greece was the diameter of the earth was 5200 miles. He fudged which units used to say about 4500 miles. This gives a diameter about 13,500 miles.
He took Marco Polo’s diaries and “calculated” how far he travelled - saying, China was 10,000 miles from the Atlantic at Portugal. (In fact, from the westernmost Africa to easternmost mainland China is 8,000 miles eastward). So Columbus expected to hit land within 3,500 miles and probably did not have enough provisions for a much longer voyage.
One suggestion is that Basque fishermen had been fishing the Grand Banks off Newfoundland for a while, but didn’t tell anyone about their favourite fishing spot. (“Did Columbus know” has been beaten to death in other threads) It makes sense, the Gulf of St Lawrence and the Grand Banks before Anglo-European industrial overfishing was incredibly rich. One theory is Columbus heard about this, and figured that was unknown wild shores north of China and Japan…
Triana not Traina 
I knew this of the top of my head because it is, or was at the time, drilled in our heads at school “On October 12th 1492 Rodrigo de Triana saw land and yelled ‘Tierra!’”.
Which produced the easy joke about Rodrigo de Tierra yelling “Triana!”.
It’s far more likely, that they would pick up the Southeast trade winds in the Pacific which would take them to the Marquesas and Oceania. It covers a much broader area of latitude and they’d would probably be sailing off the coast of that unnamed southern continent we know as S America where they’d pick up the SE trade winds
Columbus was an awful man, there is no doubt. But how was he rated as a sailor and a navigator?
The major question I have with the OP is what would the major ocean currents look like if Mexico wasn’t there? That would have a major impact, don’t you think?
Mexico would be there as it’s part of NAmerica. The gap as mentioned by the OP takes out Central America but yeah you’re right. Perhaps the currents would be flying through two continents and Columbus would have to raise extra sails.Or the current would be confused and Columbus would drown in a whirlpool.
Waiting on just the facts ma’am.
I knew it of the top of my head because Triana is a neighbourhood of Seville, and I’ve visited it - unsurprisingly, there is, in Triana, a statue dedicated to the memory of the famous Diego who hailed from there:
I don’t know about the quality of his sailing skills. Presumably, since he risked his own life, he was excellent at self-deception when dreaming up a reason to go west… (life is peaceful there.)
The educated classes of Europe were well versed in the real numbers and this is why he had trouble getting financing for his voyage. I suppose the problem with the literati was a failure of vision, to think maybe there was something out there in the vastness.
I’m curious regarding replies to my post on Columbus and telescopes. What do you people think
meant?
As mentioned above, I was only inquiring about how long he could be at sea before getting into trouble. The world-building question about what would happen to the ocen and air currents, and therefore what effects such a change would have had on the larger scale of weather, world culture, and plate tectonics, I leave to denizens of other forums to exercise their imagination with. Or see if Randall Munroe would like to write about it
Ya know, at one time there used to be a gap between N and S America. Then along came a bunch of volcanoes and filled it in with an isthmus. Columbus only missed that gap by some 2.5 to 3 million years.
Between that temporal miss and not even finding either of two pretty darn big continents, I’m gonna suggest he’s probably about as a good a navigator as this goofball: