In light of the above, may I ask what exactly you believe the Protestant term "Sola Fide" means? If your below is the interpretation, then I do not think it means what you think it means. :)
In the historical context, +Paul expected the end of times to come at any moment, and faith was a must in order for the coverts to be baptized. Under such urgency, works of faith simply had a secondary meaning to him.
Paul was correct, the end of times may come at any moment. But, I expect you mean that Paul thought that the end times were imminent to his time. I don't agree with that, but for the sake of argument, let's say that is correct. In that case, if Paul thought it was imminent, then why does he say NOTHING of specifically baptizing infants before it's too late? Converts could convert using their own free wills, so the argument goes, i.e., it was on them. Infants were completely helpless and innocent, their salvations were completely out of their hands. Why then, does Paul not scream from the mountain tops "Baptize your infants to save their souls while there's still time!!!"? I know the answer. :)
Paul knew that several of the fledgling churches weren't fully with the program yet, so the standard answer of "well everyone already knew to do that so it wasn't necessary to say in the Bible" doesn't work. Time was of the essence, yet he was silent.
But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.(Rom.4:3)
Nothing could be more clear-Sola Fide-Only faith.
Saved by faith and not works.
Paul was correct, the end of times may come at any moment
Christ, who was an apocalyptic Jew, told His disciples that some of them will not even die (and that within this generation) the end will come.
+Paul was an apocalyptic Jews and belieevd the "end" was at hand. That's why faith was much more important than works, as there was no time for works (of faith0 but faith itself was a priority.
Of course, the generation passed and all who heard or thought they heard Christ predict the end (that part is neatly attenuated later on when He says that only the Father knows...oooh more Trinitarian discord) actually did die. The Chuch then had some 'splanin' to do. But they were always good at it. :)
Why then, does Paul not scream from the mountain tops "Baptize your infants to save their souls while there's still time!!!"?
In that case, if Paul thought it was imminent, then why does he say NOTHING of specifically baptizing infants before it's too late?
In 1 Cor 1:16 he says that he "baptized the household of Stephanas." That doesn't preclude baptizing infants. Besides, he didn't think his mission was to baptize.