Car wont go in gear for a good 15-20 minutes

Hello,

There are few reason this can happen.
First you always want to make sure you have correct level of transmission fluid and the fluid is in good condition.
This can also happen due to faulty shift solenoids. The transmission uses pressure form the fluid and electronic solenoids to shift gear. If there is an issue with one of the other the vehicle could experience trouble shifting.

As the transmission warms up the fluid and other components warms up as well and it starts to work.

You might find this article helpful:

https://www.2carpros.com/articles/automatic-transmission-problems

I have attached diagrams for your reference.

Please let me know of any questions.

Thank you.