Gmail accounts have throughput limits, no matter the version you are utilizing. G-Suite accounts have higher limits, since they are paid versions.
Here are 2-dozen or so sources and links you can use to warm-up or temper your new GMail accounts by subscribing to these newsletters and have daily emails sent to your inbox.
After you have created your new GMail account, use it to sign up for some or all of these sources of frequent inbound traffic and messages into your inbox.
On some of these sites, you will need to scroll to the bottom of the page to find the subscribe button.
This should take about 20 minutes to setup all of the inbound emails you will ever need.
Please remember to verify or confirm your subscriptions. You know the drill.
http://www.foxnews.com/alerts/subscribe.html
http://mashable.com/subscriptions/
https://www.searchenginejournal.com/podcastnewsletter/
http://searchengineland.com/
https://moz.com/moztop10
https://blog.hubspot.com/
http://newslink.reuters.com/join/subscribe
https://techcrunch.com/
http://www.bloombergview.com/?subscribe-form=early_returns
http://www.bloombergview.com/?subscribe-form=share_the_view
http://link.mail.bloombergbusiness.com/.../prophets-signup
https://www.bloomberg.com/view/?subscribe-form=levine...
http://www.huffingtonpost.com/newsletters
https://www.engadget.com/thanks/
https://www.buzzfeed.com/news
http://pages.email.bbc.com/subscribe
https://account.usatoday.com/newsletters/
http://www.nytimes.com/marketing/newsletters
http://www.si.com/
http://link.billboard.com/join/38q/bb-signup
https://www.getresponse.com/features/email-creator.html
https://www.constantcontact.com/emai.../newsletter-templates
https://login.mailchimp.com/signup
http://www.theskimm.com/
https://conservativedailypost.com/
http://www.smilebox.com/lp/newsletter.html
http://www.ilovefreesoftware.com/