I take the temperature of the formula right before feeding to make sure it’s the right temperature, but the water bath for the syringe is a good idea!Sorry I don't have time to read all the replies to this post so I may repeat advice.
As for the possibility of sour crop, feed a Papaya wash. See this video for instructions: How are you ensuring that the food is being fed at the correct tenperature? You should take the temperature with an instant thermometer but also have it in a water-bath, the water at 104-5 F.
Unfortunately, a homemade brooder is probably not good enough for a day one chick. It may work out, but you'd save yourself a lot of aggravation by getting a small professional one such as this: Amazon.com : Brinsea Products TLC-30 Eco Brooder Intensive Care Unit for Young, Sick Or Injured Birds & Small Animals, Off White, USHD380C : Pet Supplies
If the brooder is at a constant temperature, slow crop can be largely avoided.
How are you ensuring that the brooder is humid enough? It is a good idea to put a clean, wet sponge in the corner. Re-soak when needed.
How are you disinfecting everything? Chicks that have never been fed by their parenta have very little immune systems and need to be kept in sterile environments. You can get F10 or use a 1:10 bleach solution. Remember to rinse anything you disinfect after a contact time of about 10 minutes. Bleach also may not be good for your syringe.
I'm going to disagree with a few of the previous comments and say that such a young chick should be kept in a small plastic or glass container inside the brooder with kleenex bedding. Change the kleenex at each feeding.
The Brooder I have right now is at a constant temperature, the heating pad is set and it keeps itself around 96-98°.
I have a hygrometer(is that the right word? The thing that measures humidity lol) along with a thermometer inside the nest, both temperature and humidity look good.
You think I can let her go 4-6 hours for her crop to empty? It’s been a little over 3 at the moment and it’s still a bit full