The Ottomans could probably colonize America if they invested more in spreading their religion through trade and such, perhaps if they conquered more land it could lead them to send ships off west, towards the Americas.
It is not impossible for the Ottomans to rule over parts of the Americas. But it will likely be different than the European one.
For one, the first contact will be mercantile. Merchants settling on the Coasts of Mexico to trade with the Aztecs and Mayans. Introducing tradegoods that could help one to overcome the other such as muskets, horses, Iron etc.
Settler Colonies might likely be a penal colony. Unwanted figures/groups can be sent to settlements in the Caribbean. Although the latter is somethings the Europeans had as well.
Pirates bases on small Caribbean Islands. Especially if the Spanish dominate the Caribbean. But this is something I imagine, the chances of this to happen is pretty much unlikely.
And all this will only work if the Ottomans do not occupy Hungary without destroying Habsburg Power for at least a Century. Ideally is no Ottoman-Hungary. Ottoman Italy (Central and Southern Italy, North is vassalised) would also be a good option to execute Ottoman possesions in the Americas.