The way adoption process works in Lithuania is that after the vetting process you are put in a queue. You can also define some preferences about who you want to adopt - age, gender, health status, are you open to adopting more than one kid, etc. Whenever a kid becomes eligible for adoption, they go through the queue and get offered to the first family who's priorities they match. The family has some time to decide if they want to accept the offer, or reject it. If the offer gets rejected, the kid goes down the queue to the next matching family, until they get accepted. If they reach the end of the queue, the kid stays in foster care.
When we got in the queue (around Christmas), we were no. 47 in the list, so we expected we'll have to wait quite a while for the first offer. So we were quite surprised to get it my mid January. Apparently it depends a lot on how specific you are with your preferences. If you tell you want a completely healthy blond baby girl under 6 months old, you can stay at the top of the list for a long time. We were quite vague - under 2 years old, can have some health issues - so the first match came really quickly.