How do I start NVDA automatically on the sign in screen?

To have NVDA automatically start during signin, press insert N to go into the NVDA menu. select settings and press enter. Once in settings, you'll be in the general section. in the general section, press tab until you find the option that reads something like: "Automatically start NVDA after signing in," and press space to check it. Once checked, press tab until you hear NVDA say apply, then press space to activate, then press enter to save the changes. then, press insert N to open the NVDA menu again, and press down errow until you hear NVDA say: "save configuration," and press enter to save the configuration. you can also press insert plus control plus C to save the settings. HTH.

NVDA on lock-screen is sometimes slow, doesn't strait away start speaking. Use Narrator for lock-screen, and set NVDA to start automatically once login successful.
As long as you don't need to frequently deal with admin permission screens, this approach is fine. Even for basic UAC screen, since they make a noise, and you can pritty much press Alt+Y if you know what you are doing, NVDA not speaking on those screens won't be that big of a issue.