It's probably not a solution now, but for the future you should recognize your daughter as being your daughter. I have a Thai girlfriend + daughter, and can get a visa for that in my home country. But cannot extend that in Thailand for a year because my name is on the birth certificate, but despite of that they do not consider me to be the father. You have to go to court for that if you are not married.
I arrived yesterday. It took a couple of hours at the airport, which irritated me after travelling for 16 hours. I did worry before leaving. But everything is fine now. Make sure that you have multiple copies of everything. They were asking people where they were going to stay after the quarantaine hotel, and even wanted documents about your booking for that. That was the only difference at immigration compared to previous times. I told them that I was going to stay at a girlfriends condo, so I did not have documents of that, only the address, and that was enough for them.
And these Thai embassy employees told you in English? 😂 Thainglish? The reason why I keep going on with this is because you are wrong, you probably didn't understand what they were trying to tell you, probably because most of them hardly speak any English, and because I think you are giving advice here which can get people into trouble.
If you think about this logically, it should be clear even without the above links. Planes fly. They have been doing that for years. You can buy tickets. That has also been possible for years. The only thing you show with a print screen is just that. What they want is proof that you have a ticket that allows you to leave the country. That is what they want to see.
For UK citizens: Immigration officials in Thailand may ask you for proof of onward travel (e.g. a return or onward air ticket). You should make all reservations before travelling to Thailand. Some airlines have refused to board passengers without evidence of onward travel.
PROOF of onward travel. You need to PROOF that you are able to leave Thailand.
on the website of our consulate they say that you need to show a confirmed flight. Making a printscreen during the order process isn't what they ask for. The reason they ask this is that they want to be sure that you are able to leave. Again, a printscreen of something you see during the order process and before paying is not what they ask for. That printscreen isn't a valid way to prove that you are able to fly home.