gktsck answer shows that the general intent to reach India was already there. But to understand how the general intent become a tangible aim, note that the path to India did not go through today's Ivory Coast, Nigeria, or Fernando Po. It went though Brazil, due to the direction of maritime currents.
What you have to look for is "When the Southern Atlantic "Volta do Mar" was discovered and mapped?'
... in the South Atlantic with the exception that the South Atlantic gyre circulates counterclockwise. As India-bound Portuguese explorers and traders crossed the equator with the intention of passing the entire western coast of Africa, their voyages took them far to the West (in the vicinity of Brazil.)
Before mapping the Southern Atlantic currents, "is it possible to go to India?" was just looking to a world map and wondering if there is some way - even the ancients could to that. After mapping the currents, they actually knew how to go south, and, instead of sending a few exploring ships in secret, they could risk a larger fleet (Vasco da Gama had 4 ships) to actually make history.
I doubt you will find an exact answer due to the secrecy imposed in the time and the loss of relevant secret documents from Portuguese archives through the centuries (*).
Even today people debate if Brazil was discovered before Cabral. A possibility is that they discovered and used the Volta do Mar to go to South Africa and India, and afterwards Cabral by chance went a little further west and found Brazil. (the official history).
Another possibility is that previous voyages had found signs that some land was nearby, and then Cabral used his voyage to India to purposely go further west and find the new land. Or, that they already knew Brazil was there and Cabral just claimed it publicly.
What is apparent is that they never stopped trying. We can assume that when they were in West Africa, Cape Verde, etc, they were also mapping Atlantic currents. Columbus voyage also depended on such knowledge and how he got that knowledge is also subject to debate today (he departed from Canarias).
(*) I was reading more and it appears "many secret documents were lost in a fire" is a Brazilian over-simplified historical legend which appears in popular sources and may refer to 1755. The Portuguese archives lost documents due to various events such as place changes, wars, and the 1755 earthquake. In 1755 the tower collapsed, but documents were recovered from the rubble.