Before iOS 15.4, quickly initiating "Emergency SOS" required users to press the lock button 5 consecutive times at a rapid speed. However, with the newest iOS update, there's a simpler way to contact emergency services.
How to call Emergency SOS faster on iOS
Your iPhone can be unlocked or locked
Press and hold the side (lock) and volume buttons until a countdown ensues.
At that point, your iPhone has done all the work, all you'll need to do is stay on the line.
When you make an SOS call, your iPhone will automatically contact your local emergency number. Moreover, you can also add emergency contacts. These contacts will also be notified through text unless you choose to cancel. They'll also be sent your location and if your current location changes.
More Information: https://support.apple.com/en-us/HT208076