Were the Gospels written to flesh out Paul's mythological Jesus? Of course not.
The Gospels tell a story that no one in his right mind would make up — certainly not if you're trying to found, or support, a religion.
Of the many elements of the story that no one would fabricate, three really stand out to me:
1) The cross — If you've got to explain how your founder died, you wouldn't make up his execution as a criminal. And you wouldn't risk making an enemy of the government by making them look bad.
2) The women at the tomb — If you wanted to pass a story off as truth, it wouldn't star the town drunk as the witness. That's about how that society viewed the testimony of women. They would not have fabricated the women as being first to the tomb.
3) The Twelve — If you wanted to found a religion around the surviving apostles, you wouldn't make them look like buffoons. For three years they didn't understand a word Jesus said, and when He rose from the dead, they didn't believe it. You can spin up an explanation as to how this isn't fatal to the new religion, but no one would tell a story like this if they didn't have to.
There are many elements of the Gospel stories that simply don't need to be there. Why explain them away? Just don't make them up. Unless they're not made up.