I may run a-foul of the anti-conspiracy policy here, but the Portuguese kings and their advisors may have been well aware of the existence of the Americas. The one substantive finding by Gavin Menzies was turning up maps in Portugal that indicated that Portuguese ships may have well reached the Americas before 1492 (of course he attributed them to the Chinese). They had no interest in backing Columbus, were really quick to "accidentally" discover Brazil shortly after the Columbus voyages, and had gotten the line dividing the world fixed just so they could make off with Brazil. Portugal was too small to exploit any Portuguese discovery of the Americas, so had an interest in keeping quiet about it.
Anyway without Columbus, presumably at some point someone makes the trip, maybe Columbus himself with English backing. The significance of Columbus was that he really was a good sailor, so without him going first we may have had some colossal failures until someone made it across, and more importantly since he sailed for Castille he put the Spanish in the lead to take over Mexico and Peru and establish their empire, and that was obviously important. Without Spain, France would have been the most likely country to create an empire in the Americas.
I would agree we might not know some stuff but I disagree on your timeline.
First you have Bartolomé Dias in 1488, hugging the coast until he reached the Indian Ocean. This is a long and unforgiving road because of bad currents.
Ten years after, Gama does a nice arc, almost reaching Brazil and landing exactly where he needs to. I admit it's suspicious.
However, I'd think Colombus did reach there before the Portuguese. If not, the Portuguese might have claimed it and bullied the Pope so they could have it instead of Spain. If they had reached it before 1492, they would only have to point out to a Padrao that surely they'd have erected.
The fact they didn't claim a padrao tells us they didn't reach the Americas.
Then, why not between 1492 and 1500? Well, they first wanted to make sure they could reach India and that Spain wouldn't follow them. If the African road was a bust, they wanted to make sure they'd have as much resource as possible to get the Americas. Once they got to India, lo and behold, Cabral discovered Brazil in his next voyage
This didn't mean they didn't discover Brazil before, as you mentioned, the fact they fought for the Tordesillas line to be pushed can suggest this, but that they didn't make it official until later