I really have no idea what will ensue in the immediate aftermath of the rapture.
If I were to speculate, I agree with the previous posts that there will likely be despair, horror, and carnage everywhere that have a large percentage of believers in their society. The removal of the One who is restraining now will eventually and I think rather quickly, spread throughout the whole world.
Even places that have very few believers are still benefiting from the restraining power of full evil being unleashed now, so when the Church goes I can imagine worldwide chaos rather quickly.
Now having experienced and watched some of the effects of worldwide governments tyrannical overreach lately, I wonder what if the rapture were to occur during a so called national/world emergency event. Maybe an orchestrated long term lock down with say extended power outages. There could be few means of communication. No phones, no internet and I can imagine the reality of what took place being able to be hidden or covered up. A lot of evil things are done in the cover of darkness, both literal and figurative darkness. Of course those who are eyewitnesses could testify (maybe) but in this world now we are being conditioned to not believe our eyes and ears.
I tend to lean towards a small gap between the rapture and the start of the trib. But any amount of time that is given to those left behind is still time within Gods grace and mercy for more to repent.
Yes those who have heard but rejected the Truth might come to faith but I'm not convinced even that will drive a huge number to receive His salvation.
I think the judgements of God being poured out might wake more up if they haven't already been hardened by the delusion. The two witnesses, the 144,000 and the angel proclaiming the everlasting gospel (and combined all that they reach) I believe will create the biggest harvest of believers.
Many will die for that new found faith, many will populate the Millennial Kingdom.
ETA: I see you two, Andy and TT, have already worked out the finer points while I was 2 finger pecking at my keyboard.