I applied in Thailand and if I recall correctly, that is why it took a while as once you apply for the affirmation to marry.the consulate then need to wait to see if there are any objections ..I think it was a wait of two weeks. If no objections are raised, then they issue you with the required docs for you to go ahead with the marriage.
Cert of no impediment is where ypur intention to marry is announced and shown that there are no objections raised by third parties as to why you can't marry.
I was in Thailand 🇹🇠when I got mine from the British Consulate there. It was such a long time ago but I recall it took about a month to get that affirmation. I am not sure if you'd be able to get the affirmation from here before you go?