For me it took about 20 minutes to get my pre-approval. Then once I submitted the remaining documents they approved it and sent me the COE within about 4 hours.
I did accidentally bring an air rifle into Thailand in a container too, I didn’t know at the time it was illegal. I just kept it in the house and used it in the yard from time to time. Never had any issues. If you do bring it I wouldn’t recommend telling a lot of people about it. Also, I think it might be legal even if you can find plastic pellets for it as from my understanding the difference between a gun which requires a license and one which doesn’t is whether or not the projectiles are metal. High power BB guns with plastic, gel, or glass ammunition are legal.