Is this delay what you see in betaflight GUI on the receiver tab?
If that is the case then I suspect that it also takes a while to connect to your quad and also when you change from tabs in betaflight GUI it is not instant.
The usual cause for this is when you have a device connected to the same UART port as the usb on your flight controller. Usb is usually on uart1 of the flight controller, so just make sure your reciever is connected to another UART like 3.
Hope.that helps but if not can you give me some.more details of your setup like what Rx you are using, and is is sbus/ppm etc…