It's basic knowledge. Everyone knows that Amerigo Vespucci (from Italy) discovered the Americas. Then Cristoforo Colombo came second. So, why didn't Italy colonize the Americas and let other powers do that?
First and foremost, because there was no such state as "Italy" in that period. The Italian Peninsula was composed of quite a number of different states like the Republic of Genova, the Republic of Venice, the Duchy of Milan, the Papal States, the Kingdom of Naples, etc.
Christopher Columbus, or Cristoforo Colombo in its Italian denomination, was a sailor working for Queen Isabel of Castile, and so was Amerigo Vespucci. Both were on the Castilian crown's payroll, not under the employ of any Italian state.
Having said that, this answer of mine from 6 months ago may come in handy to explain how the Castilians and the Portuguese came to the posession of the Americas.
https://www.reddit.com/r/AskHistorians/comments/robx83/comment/hpxgmbj/
On this other thread, I explain a bit on Columbus' origins, including references to him on the payroll of the monarchs of Castile, to whom he owed his allegiance.
https://www.reddit.com/r/AskHistorians/comments/gz7nxg/was_christopher_columbus_a_jewish_portuguese/
And more on the matter of who financed Columbus' voyage
https://www.reddit.com/r/AskHistorians/comments/fhc5xs/how_did_christopher_columbus_convince_queen/
Hey there,
Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.
If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!