It's confirmed that there will be 144,000 Jewish believers in the Tribulation who are sealed by the Spirit:
I would imagine that these people, in faithfulness to God's calling, would evangelize others in the name of Jesus. Also,
strongly implies that there will be believers. (Revelation 7 | Revelation 14)
Keep in mind there will be a few scientists and INTJs ( ) who will want to investigate the rapture and find out what went on after the event. The Rayford Steele story could be real too - if your wife, brother, friend vanished and there was a bunch of cacophony in the sky, wouldn't you at least be compelled to Google it?
It might be harder to become a believer without our assistance, seeing as we're all gone, but I think some will manage it. The Bibles won't all vanish.
In all fairness, as a counterpoint I've heard that a "deluding influence" will exist after the rapture, making it harder for people to be saved, but I can't quite find the scripture for it right now. Still, there are deluding influences at work right now too, so I think some will be saved during the tribulation. Other places imply that there will be martyrs in the tribulation for Jesus.