That is not a very helpful error. And, one that does not point to a Let's Encrypt problem.
This is most likely a configuration problem of some kind. Either in your (fairly complex) mix of components. Or, perhaps even your DNS
In any case, you should first post at the github which provided that package and instructions. They know best the most likely reasons for it to fail. In fact, they may be happy to hear of real-world problems so they can improve their offering.
Let's Encrypt is an ACME Server. We don't have access to those logs. But, that is not what is important for this.
You must use an ACME Client program to request a cert. There are numerous ACME Client programs. So, the first question is which one is your setup using? I couldn't tell from a quick glance at that github doc.
A working ACME Client will report any useful error messages from the Let's Encrypt ACME Server (which is why we don't need its logs).
But, a log from the ACME Client might be helpful. Or, perhaps something else entirely is going wrong that is just triggered by activating that screen.
You are jumping to conclusions that this is a Let's Encrypt Server problem. That is highly unlikely. Still, we often help people properly configure their ACME Client or even their server program to use certs. With your setup we just don't have any info to work with. And, I can make pretty good guesses based on what I saw from that github. Which is why I referred you there.
You didn't even provide your domain name which we could have used to run some basic tests of your DNS and server comms.
This looks like it's using nginx proxy manager. Make sure your port 80 TCP traffic is reaching your server for http domain validation to work, from looking at the instructions you maybe having to forward port 80 to port 81 on the nginx server? I'm just skim reading.