My dog died last month and it took me over a month to get another one even though we are very well set up to have a dog and do right by it. But the competition these days is FIERCE because everyone who is now working from home has decided to get a dog (or cat).
Here is what I learned as I attempted to navigate this current adoption situation:
1) Rescues are swamped and get 50-100 applicants for each dog. They will go through and pick out the one they think is perfect and ignore all the others. If you are lucky they will notify you that the dog is gone but usually it's <crickets> (They often say this right upfront.)
2) Shelters are also swamped but most have a first-come, first-serve policy so if you can get an appointment with them, you will be able to get a dog if there are any left you like.
3) Puppies and small cute dogs are snapped up immediately
4) Pits, large dogs, and special needs dogs are not
5) Rescues that specialize in taking in street dogs from other countries seem to have more dogs than shelters and local rescues if you are willing to go that route. (There are pros and cons to this method.)
6) You will have more choices if you are willing to drive out of your area. (I set my Petfinder search to dogs within 100 miles.)
7) Special needs dogs are very available but you need to be careful as they often have more problems than are listed so there can be expensive surprises. (Both my dogs were special needs and both had way more medical issues than the shelter realized.)
For myself, I started looking about a week after my dog died and, at first, I was applying for dogs one rescue at a time. I quickly figured out that was never going to work so then I started applying for every dog I was even slightly interested in. I applied for about 25 dogs with about 10 different rescues and attempted to get an appointment at two shelters. Only 2 rescues even got back to me, 1 to tell me the two dogs I liked were already gone, and 1 to offer me a dog before they turned around and gave him to someone else [they wanted him adopted with his mom and found someone who could take both dogs].
I was finally able to get an appointment at one of the shelters, but by the time I got there, all but 2 of the 7 dogs I was interested in were gone. The two left were special needs and the shelter pretty much refused to show us one of them because his behavioral issues were so bad. (We weren't experienced enough to help him.)
The dog I got is awesome! But he's also 11 and has severe dental issues. And, of course, as is typical with special needs dogs, the next day I found out he had other issues that the shelter hadn't noticed. So now I have a dog with IVDD (spinal disease) which means he might need expensive surgery one day and he cost me $500 in vet bills the first week. [The dental work is going to be $1000-2000.]
Btw, you can't just go to your local shelter unannounced in most places in the US these days. They are closed to drop-ins due to COVID and you have to make an appointment. Because of that, you have a slot and they bring a dog out to see you. There isn't time to see more than 1 or maybe 2 dogs. But the shelter staff should talk to you beforehand and help you settle on your dog from the list of available ones. The shelter I adopted from was able to tell me that one of the dogs I was interested in would definitely chase my cats, as an example.