What you are missing is that Catholic doctrine and teaching is NOT solely Biblical. It also relies on the teaching authority of the pope and tradition. Catholic tradition has held for 2000 years that those closest to God on earth, now saints in heaven, have the ability to intercede for us. This is the doctrine of the Communion of Saints. For some reason Protestants typically believe that once someone makes it to heaven, they forget about us or ignore us here on earth. Not so in Catholic teaching. We are “surrounded by a cloud of witnesses” and intimately bound together in love. We pray to the saints in heaven for their help, and they respond in love. We equally pray for the souls in purgatory, and they pray for us. We are all in Communion with each other.
There is ample evidence of the earliest Christians preserving relics of the martyrs and saints, building churches over their homes or the place of their martyrdom, and asking their intercession. Are you familiar with the thousands of Catholic saints? Try loading the free app, Laudete, and start reading the Saint of the Day.
The “proof” you are looking for is in the experience of 2000 years of Catholics having their prayers answered and drawing closer to Jesus through the intercession of the saints, as well as the many, many apparitions of Mary and the saints to people confirming that prayers have been heard. Have you read about some of these?
Please consider consulting the Catechism of the Catholic Church for far more in-depth answers than we can give you here on this subject. I don’t have one handy but perhaps others can direct you to specific chapters.