A maritime Venetian Republic that was larger might have more of a chance. A Venetian unification of north Italy, say?
On the other hand, Venetian dominance of northern Italy, that would see Venice butting heads with the Papacy, France, and the Habsburgs (not to mention all of the Italian duchies and republics alogn the way) and more resources committed to fighting one side or the other, no? Even if Venice had more luck in the Italian Wars, they'd have threats on all sides, plus the Ottomans on the seas, so I'm not sure how much they'd be able to focus on a landmass halfway across the world.
Aside from that, sailing on the Mediterranean doesn't translate well to sailing on the Atlantic, so there'd have to be naval reforms to produce ships more suited to sailing the open-ocean in order to get across the Atlantic to get and protect New World colonies. For a nation without a window to the Atlantic and so specialized in Mediterranean shipbuilding, I'm not sure how eager the Most Serene Republic would be to make such a massive change. If, however, a doge was interested enough (and survived long enough to boot) to actually do that, I suppose the Venetians would be able to make an at least respectable oceanic fleet (an Arsenal for carracks and the like?).
Of course, that also relies on them being able to compete with the Portuguese, French, English, Spanish (and later Dutch) and fight off all the pirates that came along with them. And also the Barbary pirates, just to add to the fun. Assuming Aragon still gets Naples under its crown, Venice is most likely going to butt heads with at least one Iberian power just from the power dynamics in the peninsula. Based on how Spain kept neglecting Gibraltar (they had trouble preventing the Dutch from getting ships through the Strait of Gibraltar and resisting Barbary raids in the region), however, I wouldn't say that that would make Venetian Atlantic ventures impossible. Sure, it's a bit more inconvenient compared to the rest of the colonial powers who had direct access to the Atlantic, but Venice isn't immediately sunk just because of Gibraltar.
The main issue, aside from logistics, would be interest then. It relies on Venice being interested enough in trans-Atlantic affair to dedicate a huge amount of resources and manpower and redirect their focus westward which, while plausible, is a bit unlikely in the grand scheme of things (in hindsight after the Mediterranean is overshadowed by the Atlantic, sure. But by then it's a bit late and there's a fair amount of competition. And before, well, Mediterranean trade is much more profitable so not much incentive to try something new and uncertain).