How to receive new emails faster on iPhone?

I added a Gmail account to my iPhone, but it receives emails too slowly. I decided to try an experiment: 1. I plugged my phone into a charger and connected it to wifi. I turned it off, then turned it on and left it waiting on the homescreen, ready to tap it if it's about to sleep again. 2. I used gmail.com to send myself an email. I started a stopwatch after it confirmed it was sent. I checked how long it took for Mail.app on my Mac to receive the email, and I also checked how long it took for Mail on my iPhone to receive the email. I did this three times. My Mac received the email in 5 or fewer seconds every time (5s, 3s, 3s). My iPhone... after waiting for 7 minutes and the mail still hadn't arrived, I decided to stop wasting my time. After opening the Mail app, it finally refreshed itself, and pulled the new email. After opening Mail for the first time, subsequent emails (as long as the phone stays turned on for the whole period in-between) are received fast, in 5-20 seconds. The phone is charging and connected to Wi-Fi. In Settings > Mail > Accounts > Fetch New Data on my iPhone, Fetch Automatically is already selected. Gmail is using Fetch (it can only use Fetch or Manual). How can I make the iPhone receive new emails faster, even if it is sleeping or has just been sleeping?