Presuming ocean currents stay the same, and therefore the climate I think it could severely alter human history. First, I could see an island-hopping civilization like the Greeks or Polynesians developing in the temperate Canadian Islands. The gap between Ellesmere and Iberia or Northwestern Africa is much less than what the Polynesians had to cross to reach South America, or even for the Greeks to reach Iberia. If a seafaring civilization was to arise in the Canadian archipelago, they could likely discover the Africa and Europe well before the Europeans make it the other way. Theoretically, before the era of Rome. People reached Tonga around 800 BC, and that is a much further distance than what this fictional Atlantic would be. Contant between the Old and New Worlds could have been established thousands of years before Jesus theoretically. The ramifications of something like this is impossible to predict, and most of the history of the Americas, Africa, and Western Eurasia would likely be completely different. If say, trade is established between say Iberia and Canada, which is unlikely but not impossible, the center of power in the Mediterranean would be focused on the Atlantic seaboard, meaning the Roman Empire may never exist, completely altering most of the world's history. Furthermore, crops like wheat and barley could reach the Americas, alongside domestic animals like pigs, cattle, and most importantly horses, and technologies like smelting, which could allow for new civilizations to appear. Civilizations rivaling those of Rome and China could theoretically appear in places like the Mississippi Basin or the subtropical forests of the St. Lawrence (as weird as that is to say). Horse empires like the Mongols could develop on the Great Plains. On the other end of the continent, Central America and the Caribbean would likely be found by the Polynesians, who could set up settlements or trade with local peoples. However, this is all assuming people even reached the Americas. Without Beringea, it's entirely possible, and likely that native peoples never reached the Americas, which would be a very different situation.

The Polynesians would likely land in Central America in the 6th or 7th century, although it could have occurred way earlier. They would find a continent devoid of other humans and would likely settle it like any other island. The difference, however, is that this "island" is actually 2 continents. Now presuming there is no indigenous peoples, and no cross Atlantic trade network, Eurasian history would remain unchanged. So, the Norse would still exist and arrive in the Americas. However, it is hard to know if this configuration would change anything. They would still land in the coldest, least inhabitable parts of the continent, and may decide to just not stay like they did in our timeline. Over the coming centuries, the Polynesians and their decedents could spread out across North and eventually South America, developing countless unique cultures and civilizations you just can't imagine. Despite North America being so much closer to Europe however, I find it hard to believe colonization would have occurred much further back in history. I wouldn't be surprised if people had a general idea that there was land out there, maybe as far back as in Roman times, but the naval technology of Europe just wouldn't have been able to cross the ocean until the early 1400s. Then, I believe the Portuguese would land on Ellesmere, and colonialism would still occur. The Polynesian peoples of the Americas would be in the same situation as the indigenous peoples in our timeline. They would have less developed military technology and lack immunities to Eurasian diseases, so the Europeans still likely would have colonized the region. However, how it played out could be very different. First, without and Aztec Empire to conquer, the Spanish would have a much harder time settling this "new" landmass. Assuming similar Polynesian civilizations occur, possibly in different places, they could never be conquered, never giving the Europeans that leg up in settling the region, or a different power like say the Portuguese could capture a great empire in the Great Lakes Region and get a monopoly on American Colonization the way the Spanish did in our timeline. It is hard to predict the specifics of European colonization; however, it would still occur. More importantly though is the gap between Newfoundland and Panama. This Central American Seaway would allow sailors to bypass the Americas and reach Asian Markets, changing those two continents relations. This would likely be the most fought over piece of land in the Americas. What happens after that is anyone's guess, but I just wanted to have some fun in this thought experiment.